Cultural Assimilation: The Political Economy of Psychology as an Evolutionary Game Theoretic Dynamic

Virginia Military Institute From the SelectedWorks of Atin Basu Choudhary 2012 Cultural Assimilation: The Political Economy of Psychology as an Evolutionary Game Theoretic Dynamic Atin Basu Choudhary, Virginia Military Institute Dave Cotting, Virginia Military Institute Available at: https://works.bepress.com/atinbasu/24/

Original Article Cultural Assimilation: The Political Economy of Psychology as an Evolutionary Game Theoretic Dynamic ATIN BASUCHOUDHARY Department of Economics and Business Virginia Military Institute DAVE COTTING 1 Department of Psychology Virginia Military Institute Email: cottingdi@vmi.edu Abstract In this paper, we model the interaction between idiocentric and allocentric immigrants in two settings in a society that is predominantly collectivist and in a society that is predominantly individualist. Immigrants, either allocentric or idiocentric, can also be entity theorists (fixed mindset) or incremental theorists (growth mindset). We use evolutionary game theory to model how the host country cultural environment places selective pressure on the cultures of immigrant populations. This has implications for how well immigrants assimilate into their host country. Our results show: (a) depending on the initial ratio of allocentric and idiocentric immigrants, assimilation is either complete or nonexistent in collectivist societies; (b) in individualist societies assimilation is never complete (c) the lower the cost of coordination for allocentric immigrants, the easier it becomes for both allocentric and idiocentric immigrants to assimilate into collectivist societies; (d) the lower the cost of coordination for allocentric immigrants, the harder it becomes for both allocentric and idiocentric immigrants to assimilate into individualist societies and; (e) entity theorists are more likely to be favored in individualist societies. 1 Names appear in alphabetical order. 1 P a g e

Generally speaking our modeling approach can inform our understanding of the dynamic link between psychology and culture. Keywords Immigration, evolutionary game theory, allocentric/idiocentric, collectivist/individualist, culture, memes. Introduction Global migration patterns have brought diverse cultures into contact with each other. This contact has generated increased societal and political discussions about immigration. Some questions, among others, emerge from this discussion. How do immigrants assimilate into a host culture? What is the process of this assimilation? What kinds of immigrants assimilate into the host culture? We try to answer these questions using an evolutionary game theory approach where culture influences perceptions of self and the world. We suggest that our paper may have important policy implications. But more generally we think our modeling approach may be useful for investigating the dynamic links between psychology and culture. We model a society that hosts an immigrant population. The host society has a predominant culture. In the study of psychological processes, culture has been described as shared assumptions where people can predict each other s actions in a given circumstance and react accordingly (Haviland, 1975, p.6), as a set of guidelines to interpret our own behaviors, our relations to other, and the world itself (Helman, 1994), or as meaning-making as Shweder & Sullivan (1993) so elegantly capture: [Culture] is that subset of possible or available meanings, which by virtue of enculturation informal or formal, implicit or explicit, unintended or intended has become so active in giving shape to the psychological process of individuals in a society that those meanings have become, for those individuals, indistinguishable from experience itself. (p. 29). Cultures are often described along the independence-dependence continuum (Hofstede, 1980, 1991; Hui & Triandis, 1986; Kagitcibasi, 1997; Kim, Triandis, et al, 1992; Kim, Triandis, et al, 1994; Laungani, 1998, 1999; Matsumoto, 1996; Schwartz, 1990; Triandis, 1994). The fundamental beliefs about the independence or interdependence of self in 2 P a g e

relation to others had been found to shape meaning-making, and thus influence cognitive, motivational, affective, and behavioral processes. 3 P a g e In our model therefore, the host society has either a predominantly collectivist culture or a predominantly individualist culture. In individualist societies loosely linked individuals who view themselves as independent of collectives; are primarily motivated by their own preferences, needs, rights, and the contracts they have established with others; give priority to their personal goals over the goals of others; and emphasize rational analyses of the advantages and disadvantages of associating with others (Triandis, 1995, p. 2). Collectivist societies have closely linked individuals who see themselves as parts of one or more collectives (family, co-workers, tribe, nation); are primarily motivated by the norms of, and duties imposed by, those collectives; are willing to give priority to the goals of these collectives over their own personal goals; and emphasizes their connectedness to members of these collectives (Triandis, 1995, p. 2). Triandis (1995) argues that the individualism-collectivism feature refers to societies. Individuals on the other hand can be idiocentric or allocentric. Thus, individualistic societies tend to include a majority of idiocentric individuals (i.e., individuals culturally motivated to develop a sense of self based on within-person attributes) and collectivist societies tend to include a majority of allocentric individuals (i.e., individuals culturally motivated to develop a sense of self based on collective attributes). Individuals in the immigrant population in our model can therefore be either allocentric or idiocentric. Allocentric minorities in individualistic societies and idiocentric minorities in collectivist societies may consequently be described as countercultural: [ ]in collectivist societies there are idiocentrics, who look for the earliest opportunity to escape the oppression of their ingroups, and in individualistic societies there are allocentrics, who reject individual pursuits and join gangs, clubs, communes, and other collectives (Triandis, 1995, p.36). As applied to cultural assimilation, one may extend the use of countercultural to describe the mismatch that may occur between immigrants and their host culture. We therefore assume that allocentric individuals assimilate into collectivist societies. Idiocentric individuals, on the other hand, are culturally motivated to base their sense of self on within

person or individualist attributes. We therefore assume that idiocentric immigrants assimilate into individualist societies. 4 P a g e Behaviors related to cultural assimilation are also driven by goals, both at the group and individual levels, and the psychological processes that shape the pursuit of these goals prior to and during each step of the dynamic exchange between host and immigrants. These goals are not only affected by, but stem in accordance to, lay theories (i.e., implicit theories or assumptions) (Dweck, 1988, 1991, 1996, 2006; Epstein, 1989; Ross, 1989). Cultural assimilation assumes a change in one s self and one s related goals. Thus, lay theories about self and others may play an important role in the success or failure of assimilation. For our model, we relied on the extensive work of Carol Dweck, which broke new ground in our understanding of how implicit theories about human attributes can shape goals related to those attributes. According to Dweck (1991, 1996), people can be described as entity theorists - holding beliefs that human attributes and qualities are fixed and cannot be significantly changed (fixed mindset) - or incremental theorists - holding beliefs that human attributes are malleable and can be cultivated through efforts (Growth mindset) (Dweck, 2006, p. 7). Further, a fixed mindset is likely to orient an individual towards the goals of measuring, judging, and evaluating the attribute of interest (in self and others), whereas a growth mindset is likely to include goals related to the development of that attribute (Dweck, 1996). Thus, to understand cultural assimilation, it may be essential to consider the implicit theories about the malleability of idiocentrism and allocentrism in self and others, and perhaps more generally cultural identity. One s idiocentrism/allocentrism is expected to influence how one makes appraisals of costs and benefits in the pursuit of the goal to assimilate into the fabric of a different culture; one does not simply assess the cost and benefit for self, but appraises it through the lens of her/his idiocentrism or allocentrism. Immigrants, in our model, therefore have either an entity or incremental theory of allocentrism/idiocentrism. This diverse immigrant population can find themselves in one of two types of host societies collectivist or individualist. We claim that idiocentric immigrants who learn to be allocentric in a collectivist society have assimilated. Similarly, allocentric immigrants who learn to be idiocentric in individualist societies have assimilated as well.

We use evolutionary game theory to model how host country culture puts selection pressure on the cultural values idiocentricity/allocentricity of immigrant populations. This incentivizes individuals to learn (or not) to assimilate and changes the initial mix of the immigrant population. Our model predicts the final mix of immigrant types as a function of the initial mix of immigrant types and the nature of the host society. We find that our theory provides a number of surprising results. First, we find that assimilation is either complete or non-existent in collectivist societies. In other words, given the initial ratio of allocentric and idiocentric immigrants, all immigrants learn to be either allocentric or idiocentric in collectivist societies. However, in individualist societies assimilation is never complete. Moreover, the lower the cost of coordination for allocentric immigrants, the easier it becomes for both allocentric and idiocentric immigrants to assimilate into collectivist societies. Conversely, the lower the cost of coordination for allocentric immigrants, the harder it becomes for both allocentric and idiocentric immigrants to assimilate into individualist societies. Finally, our model suggests that entity theorists are more likely to be favored in individualist societies. The specific predictions of our model may have a number of practical policy implications. For example, we could argue that immigrant ghettos should be encouraged in collectivist societies to encourage assimilation, and the opposite in individualist societies. For that matter our paper could generate a policy debate on the virtues (or lack thereof) of assimilation itself. More generally though, we would like to advocate our approach in understanding how psychological traits may evolve in different societies and inform the evolution of culture in societies. In other words, we believe our modeling approach can inform our understanding of the links between psychology and culture. We describe and discuss our model in the theory section below. The last section concludes. Theory In this section, we introduce the basic structure of our model. We then derive the evolutionary stable equilibrium and discuss some implications of this equilibrium in separate sections. 5 P a g e

The Model Let there be two cultures Individualist (I) and Collectivist (G) in the immigrant population in a host country. We focus on the immigrant population and interactions between immigrants in a host country where the predominant culture may be either Individualist or Collectivist. We focus on the immigrant population as a whole because we are interested in the likelihood that immigrants are assimilated into either type of host culture. An immigrant can be a member of either culture I or G, but not both at the same time. 2 Immigrants interact in a society the game that has these two cultures as the strategy set. Immigrants receive payoffs that are interpreted as the fitness of their respective cultures. Fitness tracks the likelihood that a particular culture will prevail in a population. Fitness depends on certain parameters grounded in lay theory described below. Players from both cultures interact in random parings. In these pairings, the agents play strategies based on their culture (Smith, 1982). Players, as is commonly accepted in evolutionary game theory, are boundedly rational in the sense that individuals do not change their strategy. However, fitter strategies are learned over time and therefore propagate faster through the population. In other words, people in our model are rational in the sense that they have consistent preferences. But this rationality is bounded in the sense that as more information about events fitness of a particular strategy at a point in time, for example is available, people update their preference ordering to take into account this new information. Thus rationality (i.e., the preference ordering of individuals) is state dependent (Gintis, 2009). While we make no formal claims about this updating or learning process, we do assume that immigrants who hold an entity theory about idiocentrism-allocentrism (i.e., individuals who believe this attribute to be fixed) are less likely to learn to adapt to a host culture than immigrants who hold an incremental theory of idiocentrism-allocentrism (i.e., individuals who believe this attribute to be malleable). 2 Of course, individuals may theoretically be characterized as standing at the mid-point of the individualism-collectivism continuum. We argue, for the sake of mathematical tractability, that a predominance of idiocentric individuals in a society characterize a culture as being individualist, and a predominance of allocentric individuals as being collectivist. 6 P a g e

Each player s fitness can have up to three components. Allocentrism provides both collective and individual benefits. Idiocentric individuals only consider benefits for themselves. Thus, allocentric individuals get a benefit, B G, when they interact with other allocentric individuals. One can view this as the synergy one gets from being allocentric in a collectivist culture. Allocentric individuals also get an individual benefit, B I, from their collectivist culture. 3 However, idiocentric individuals get a benefit B I too when they interact with allocentric individuals. 4 This modeling approach explicitly takes into account the possibility that idiocentric individuals can free ride off allocentric individuals or in collectivist cultures. In addition, there is an explicit cost for coordinating or matching with other allocentric individuals, C A. 5 We do not explicitly model a cost for when idiocentric individuals coordinate with other idiocentric individuals, effectively normalizing this cost to 0. The overall results of the game do not change given the parameters described here and the assumptions we make about their relative sizes below, as long as we assume that idiocentric individuals coordination costs are lower than allocentric individuals coordination costs. This assumption is plausible because idiocentric individuals, by virtue of their nature, do not want to coordinate with others and therefore do not bear coordination costs. Thus if two allocentric immigrants interact, they both get the individual benefit B I and the benefit from coordinating with other allocentric individuals, B G. As expected, both also bear the coordination costs. Thus each of these players fitness is B G + B I -C A. However, if an allocentric immigrant interacts with an idocentric immigrant, then neither get the benefit from Collectivism effectively then, B G = 0. Both individuals, however, get the individual benefits B I. Of course, only the allocentric individual bears the coordination costs, C A. If two idiocentric immigrants interact, then they bear neither the cost nor 3 One can think about this statement in the context of a car insurance system: everyone who pays into the system gets a benefit when they get into an accident that is someone else s fault, but they also get a collective benefit as more people join the risk pool, thus reducing the risk premium. 4 To continue with the car insurance example, individuals who do not join an insurance pool get an individual benefit when they get into an accident that is not their fault when the other party is covered by insurance. 5 Again, in the context of the car insurance example this would be the premium paid by the people who buy insurance. 7 P a g e

benefit from Collectivism. We normalize the fitness of such interactions to 0. This basic game is represented in Table 1. Note Table 1 represents an evolutionary stage game and is not a normal form representation. Table 1. The Evolutionary Stage Game. Allocentric (G) Idiocentric (I) Allocentric (G) B G + B I -C A, B G + B I -C A B I -C A, B I Idiocentric (I) B I, B I -C A 0,0 Notice that we are basically modeling a coordination process. Thus our game is basically a coordination game. The game differs in a collectivist versus an individualist society in the returns from coordination. Increasing returns to coordination, in this context, give us a well known assurance game. Alternatively, constant returns to coordination and decresing returns to coordination give us a prisoner s dilemma and a chicken game respectively. These are all well known classes of games and we will not describe them any further here. 6 In fact for each of these games the evolutionary outcomes are also well defined (see e.g. Harrington, 2009). Our modeling innovation, to the best of our knowledge, lies in our interpretation of these games in an evolutionary setting. Using allocentrism/idiocentrism in an evolutionary setting is new as far as we know. We solve for both evolutionary stable strategies and predict evolutionary dynamics. We do this for two cases when there are increasing and decreasing returns to coordination. We argue that the returns to coordination are determined by the predominant culture of the host society. Thus in an individualist society B I > B G. However in a Collectivist society B I < B G. Thus, we argue that in a collectivist society there are increasing returns to individuals from coordinating with each other. This is reversed for an individualist society. For the purposes of this paper such returns are exogenously determined. 6 Any well-known game theory textbook will talk about these classes of games in detail. 8 P a g e

The Evolutionary Stable Equilibrium 9 P a g e Recall that in our model, we have a population of immigrants who are either idiocentric or allocentric (i.e., part of an individualist or a collectivist culture respectively). Immigrants, of course, come from different countries and presumably different cultural traditions. Therefore, our model focuses on an immigrant population as a whole because we want to investigate the likelihood that immigrants will be assimilated in a wider host culture. These immigrants interact in one of two host cultures one where the host culture is predominantly allocentric (i.e.,collectivist culture) and another where the host culture is predominantly idocentric (i.e., individualist culture). We ask whether these immigrants are likely to assimilate with the host culture as they interact with each other. Thus, because immigrants can be either idiocentric or allocentric, we may ask if immigrants will learn to be allocentric in a predominantly collectivist host culture. Similarly, as immigrants may be from either individualist or collectivist cultures, we may ask if they will learn to be idiocentric in a predominantly individualist host culture. To answer these questions, we first derive the general conditions for when one orientation (i.e., idiocentrism or allocentrism) is fitter than the other. The fitter orientation of course will propagate faster. We therefore use the replicator dynamic approach to determine the ESS. We then apply these general conditions to the two kinds of host societies predominantly individualist culture and predominantly collectivist culture. We find that assimilation is not guaranteed in either sort of host culture and depends critically on the proportion of immigrants of a particular orientation relative to the immigrant population as a whole. The General Conditions: The ESS. Let the x be the proportion of the immigrant population that is allocentric. Therefore 1-x is the proportion of the immigrant population who is idiocentric. Two members of the population are matched at random with each other. Therefore the expected fitness of the behavior of an allocentric immigrant (i.e., immigrant from a collectivist culture) is: E(C) = x(b G + B I -C A )+(1-x)( B I -C A ) (1) And the expected fitness of the behavior of an idiocentric immigrant (i.e., immigrant from an individualist culture) is:

E(I) = x B I +(1 x)0 = x B I (2) The relationship between E(C), E(I), and x are simulated in Figs. 1, 2, 3, 4, and 5 below for specific values of B G, B I, and C A that are consistent with the assumptions we make about our characterization of either type of host culture. Setting (1) = (2) we solve for x. This gives us the proportion of allocentric individuals x* in an immigrant population for which neither orientation is fitter (See e.g. Harrington (2008) pp. 513-514 for a description of how this process works and why it is justified in this case). Thus, (3) We now apply this general condition to each one of the host cultures. Recall that our characterization of the host cultures as predominently collectivist or individualist is predicated on whether B G > B I or whether B G < B I respectively. Case 1. Host Culture is Predominantly Collectivist (B G > B I ). We further assume in this case that B G > C A. We therefore make an additional assumption about the costs of coordination for allocentric individuals relative to the benefits possible. We argue that costs of coordination for allocentric immigrants in a predominantly collectivist society is less than the synergistic benefits of allocentrism in a collectivist culture precisely because this host society is predominantly allocentric. The benefits of being allocentric in a collectivist society outweighs the costs. Thus this particular assumption merely characterizes a host society that is predominantly collectivist. First, notice that our characterization of a collectivist host society implies that B G - B I > 0. This means the denominator for the x* expression derived in (3) is positive. Now notice that if B I > C A then the numerator for the expression in (3) is negative. However, if B I < C A then the numerator of the expression in (3) is positive. Further, it is trivial to show that as long as B G > C A (which is true because of the way we have characterized a predominantly collectivist host society) the numerator will always be smaller than the denominator thus ensuring that x* < 1. All this gives us: 10 P a g e

Remark 1: x* switches from a positive to a negative fraction depending on whether B I < C A or B I > C A respectively (i.e., as C A falls). Now notice that because B G > B I, the slope of (1) exceeds that of (2). This is represented in both Figs. 1 and 2 for a specific set of values for B G, B I, and C A. Figures 1 and 2 show the relationship between E(C), E(I) and x. Thus if the actual proportion of allocentric immigrants x > x*, then E(C) > E(I). In this case the proportion of allocentric individuals will rise in the immigrant population. Since the host culture is predominantly collectivist, this means that these immigrants are being (culturally) assimilated. However, if x < x* then E(C) < E(I). In this case the proportion of allocentric individuals will decline in the immigrant population until the entire immigrant population is idiocentric. This means that the immigrant population over time will not (culturally) assimilate into the host culture. Moreover, recall from Remark 1 that as C A falls, x* changes from a positive to a negative fraction (i.e., x* becomes smaller as C A falls). Thus, as C A falls the assimilation of the entire immigrant population becomes more likely even if the initial proportions of allocentric immigrants are small. Of course, the proportion of allocentric immigrants x cannot ever be negative. Thus, as C A falls so that x* < 0, then all possible proportions of allocentric individuals within the immigrant population will exceed x*. In this situation, immigrants from either orientation/culture will always assimilate. 7 These results are simulated in Figs. 1 and 2 below. In Fig. 1, B G =16, B I =4, and C A = 12. Here, if the proportion of allocentric immigrants is higher than x* = 0.67, the entire immigrant population will assimilate into the collectivist host culture. However, this assimilation will not happen if the actual proportion of allocentric immigrants is less than 0.67. 7 Notice here that if B G <C A then x* > 1. This merely means that E(I) will always exceed E(C) making collectivism/allocentrism an impossible equilibrium for acculturating individuals. We eliminate this possibility by our assumption that B G >C A in a collectivist host society. 11 P a g e

10 8 6 4 2 0-2 -4-6 -8 0 0.2 0.4 0.6 0.8 1 1.2 E (C) E(I) Figure 1. B G =16, B I =4, and C A = 12 But as C A falls to (for example) 2, this situation changes. This change is illustrated in Fig. 2. Notice here that for all values of x, E(C) > E(I) since x* = -0.17. 20 18 16 14 12 10 8 6 4 2 0 0 0.2 0.4 0.6 0.8 1 1.2 E (C) E(I) Figure 2. B G =16, B I =4, and C A = 2. Thus, the immigrant population will always assimilate if C A is this low. This discussion leads to: 12 P a g e

Remark 2: Assimilation of immigrants is more likely as the cost of coordinating with other allocentric immigrants falls. Notice that Remark 2 implies that clusters of immigrants may actually encourage assimilation into a collectivist host culture to the extent that these clusters reduce the cost of coordination among immigrants who come from the same collectivist culture. But this has important implications for the persistence of culturally determined lay theories about the malleability of idiocentric/allocentric beliefs about self and others. Recall that immigrants of either culture collectivist or individualist may have either an incremental or entity theory about the malleability the related orientation (i.e., idiocentrismallocentrism) in self and others. But our results in this section suggest that, depending on the initial distribution of idiocentric and allocentric immigrants and the costs of coordination between allocentric individuals, these individuals can learn to be all allocentric or all idiocentric. Thus any immigrant who cannot learn will be in a sub-optimal culture and will literally be marginalized and expected to ultimately disappear from the immigrant population. This suggests that only immigrants with incremental theories may persist in a collectivist host culture irrespective of whether they assimilate or not. This leads to: Remark 3: immigrants with an entity theory of idiocentric/allocentric beliefs about self and others are unlikely to succeed in a collectivist host culture. Case 2. Host Culture is Predominantly Individualist (B G < B I ). In this case, we make no restrictions on the costs of coordination for allocentric individuals relative to the benefits from being allocentric since we are modeling a host culture that is predominantly individualist. The numerical simulations for our results are represented in Figs. 3, 4, and 5. Notice first that for this host culture, the denominator for the expression in (3) is always negative. However the numerator can be negative or positive depending on whether B I < C A or whether B I > C A, 13 P a g e

respectively. Also note that because B G < B I the slope of (1) exceeds that of (2). These conditions predict three possible ranges for the value of x*. First, when C A > B I, then x* < 0. Thus, since the slope of E(I) exceed the slope of E(C), the expected fitness of idiocentric immigrants will always exceed the expected fitness of allocentric immigrants. Therefore, whatever the initial proportion of allocentric immigrants in this culture, ultimately all immigrants will assimilate into the individualist host culture. This is represented in Fig. 3 for B G =4, B I =16, and C A = 20. In this case x*= -0.3333 and E(I) always exceed E(G) for all possible proportions of allocentric immigrants (0 1). Notice that all immigrants will evolve into the individualist culture and therefore be assimilated. 20 15 10 5 0 E (C) E(I) 0 0.2 0.4 0.6 0.8 1 1.2-5 Figure 3. B G =4, B I =16, and C A = 20. But if C A falls so that B G < C A < B I, then 0 < x* <1. However, given the slopes of equation (1) and (2) for any x > x* then E(I) > E(C). Thus for any x > x* the proportion of idiocentric individuals will rise in the immigrant population, replacing allocentric immigrants. Effectively, allocentric immigrants will learn to be idiocentric since idiocentric behavior is fitter, and assimilation will proceed until the 14 P a g e

proportion of allocentric immigrants reaches x*. Similarly, for any x < x* allocentrism will be incentivised even though the host culture is individualist. Clearly in this situation, the immigrant population will not be completely assimilated and the proportion of allocentric immigrants will rise until it reaches x*. In this situation, a certain proportion of immigrants, x*, will never assimilate into the individualist host culture. This is represented in Fig. 4 where B G =4, B I =16, and C A = 12. Notice that x* = 0.33 in this case. Thus, if the actual proportion of allocentric immigrants is 0.1, then over time the collectivist culture will be fitter than the individualist culture until the proportion of allocentric immigrants equals 0.33. However, if the proportion of allocentric immigrants exceeds 0.33 for example 0.5 then idiocentric immigrants will find their behavior is fitter and the proportion of allocentric immigrants will fall until, once again, their proportion is stable at 0.33. Thus in this case, 33% of immigrants will remain unassimilated in a host society where the culture is predominantly individualist. 18 16 14 12 10 8 6 E (C) E(I) 4 2 0 0 0.2 0.4 0.6 0.8 1 1.2 Figure 4. B G =4, B I =16, and C A = 12. If C A falls to the point where C A < B G, then x* > 1 and E(C) always exceeds E(I) for all values of x (0 1). Thus, allocentric behavior will always be incentivized in this case and no immigrant will ever be assimilated into the individualist host culture. This is illustrated in Fig. 5 below, where B G =4, B I =16, and C A = 2. Notice in this case that x* = 1.17. Further, E(C) > E(I) for all values of x ( 0 15 P a g e

1). Thus, for example, even if the initial proportion of allocentric immigrants is 0.1, the proportion of allocentric immigrants will rise until all immigrants are allocentric. 20 18 16 14 12 10 8 6 4 2 0 0 0.2 0.4 0.6 0.8 1 1.2 E (C) E(I) Figure 5. B G =4, B I =16, and C A = 2. In this case, no immigrant will be (culturally) assimilated. This discussion allows us: Remark 4. As C A falls x* rises. Remark 5. Both orientation in the immigrant population idiocentrism or allocentrism can potentially persist when the host culture is individualist. Remark 5 may also have an important consequence for the role of lay theories about the malleability of idiocentric/allocentric beliefs in self and others. If a certain proportion of allocentric individuals can coexist in equilibrium with idiocentric individuals, then clearly all immigrants do not have to learn to adapt their orientation. In other words, entity theorists can persist in an immigrant population when the host culture is individualist. This leads to: 16 P a g e

Remark 6. Immigrants who have either an entity or incremental theory of idiocentrism/allocentrism in self and others can persist in a host society with a predominantly individualist culture. Conclusion We postulate in this paper that immigrants are heterogenous in that they can originate from either an individualist or a collectivist culture (and thus develop either idiocentric or allocentric orientations). Immigrants from both characterized cultures may find themselves in a host society that can be either individualist or collectivist. We then argue that whether immigrants are assimilated into a host culture depends critically on the initial proportion of allocentric immigrants as well as the costs faced by these individuals when coordinating with other allocentric immigrants. We find several surprising, and testable, results. For example, it is not clear that immigrants will be assimilated into a collectivist host society, even when the costs faced by allocentric individuals when coordinating with other allocentric individuals is lower than their benefits. Of course, assimilation into the collectivist host culture becomes more likely as this cost falls. On the other hand, assimilation is unclear in individualist host societies. In these societies, for a certain range of the cost of coordination between allocentric immigrants, assimilation proceeds only upto a particular point. Assimilation of allocentric immigrants into an individualist host society proceeds only if the costs of coordination between these allocentric immigrants is high indeed if these costs are low, then even idiocentric immigrants turn allocentric and assimilation becomes impossible. Last, we also make the case that while immigrant incremental theorists have a distinct advantage over immigrant entity theorists in a collectivist host culture, both immigrant entity and incremental theorists can persist in individualist societies. Our results can inform the policy debate on assimilation. We did not propose to find answers to specific answers to this policy debate. Neverthesless, our results can help frame the questions in this debate and help move the debate along a scientific path. For example, should public money be spent to help immigrants assimilate if the assimilation process is inevitable or for that matter impossible? Or, if 17 P a g e

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