Game theory and applications: Lecture 12

Transcription

1 Game theory and applications: Lecture 12 Adam Szeidl December 6, 2018 Outline for today 1 A political theory of populism 2 Game theory in economics 1 / 12

2 1. A Political Theory of Populism Acemoglu, Egorov and Sonin (2013), QJE. Many Latin-American countries had left-wing populist politicians. Hugo Chavez in Venezuela, the Kirchners in Argentina, Evo Morales in Bolivia, Alan Garcia in Peru. Populist in that they claim to defend interests of common man against privileged elite. But left-wing populist policies seem to be left of median voter s preferences, and may harm majority of voters. Example: expansive macro policies lead to crises hurting the poor. Why do politicians choose such policies, and why do they get electoral support? AES: to signal that they are not captured by the right-wing elite. When voters fear that politicians may be corrupted by rich elite, signals of integrity are useful. Honest politician seeking reelection may choose populist policies to signal that he is not corrupted. Yields comparative statics on when are populist policies more likely. 2 / 12

3 Setup Two-period model, each period politician in power sets x t R. Policies below 0 favor the poor, those above 0 favor the rich. Utility of citizen i is 2 u i (x 1, x 2 ) = (x t γ i ) 2 where γ i is from distribution G(.) which is symmetric around zero. Thus social welfare in period t is t=1 U t = x 2 t Var(γ). Each period politician in power gets W 0. Share µ of politicians honest, share 1 µ corrupt and can be bribed. Utility of a corrupt politician: v(x 1, x 2 ) = 2 t=1 {αu t + W I office t + B t I bribed t } where α > 0 is weight on social welfare and B t is bribe. Utility of an honest politician is the same except for the last term. 3 / 12

4 Setup 2 There is a right-wing lobby with bliss point b > 0 2 [ w(x 1, x 2 ) = β(xt b) 2 ] B t t=1 where β > 0 is their weight on policy relative to money. Voters do not observe type of politician. At the end of period 1 there is an election between incumbent and unknown challenger. Challenger is corrupt with probability µ. Before the election voters get signal s = x 1 + z. Voters do not observe x 1. z has mean zero and is normally distributed. Timing is as follows: 1 Politician (if corrupt) and lobby bargain; politician sets x 1. 2 Voters get signal s = x 1 + z. 3 Voters vote on which politician will come to power. 4 Politician (if corrupt) and lobby bargain; politician sets x 2. 5 All agents learn x 1 and x 2 and get payoffs. 4 / 12

5 Assumptions on equilibrium Look for pure strategy Perfect Bayesian equilibrium in undominated strategies. Undominated strategies rule out nonintuitive voting equilibria. Because of Median Voter Theorem, voting outcome will be determined by preferences of the voter with median preferences. If median voter prefers policy x to policy x, majority of voters will prefer x to x. Assumption 1. Variable z has normal distribution N(0, σ 2 ) such that σ > max(w /(4αβ), b). Sufficient noise in observations to ensure politicians maximization problem is convex. 5 / 12

6 Analysis: final period No reelection incentives, hence honest politician sets x h 2 = 0. Corrupt politician bargains with lobby to maximize combined payoff which yields x c 2 = max{w α(x c x2 c 2 ) 2 β(x2 c b) 2 } β b, and combined payoff: W αβ α + β α + β b2. Combined payoff without a relationship: W βb 2. β Hence joint surplus is 2 α+β b2. Assume politician gets share χ of joint surplus, then bribe satisfies and hence β2 α(x2 c ) 2 + B 2 = χ α + β b2 B 2 = ( χ + α ) β 2 α + β α + β b2. 6 / 12

7 Analysis: election Median voter prefers x2 h (= 0) to x 2 c (> 0) hence people want to vote for an honest politician. Voters choose incumbent iff their posterior that she is honest is at least µ. Denote x1 h = h and x 1 c = c, and look for equilibrium in which h < c. Given signal s, posterior that incumbent is honest is and ˆµ(s) µ iff ˆµ(s) = µf (s h) µf (s h) + (1 µ)f (s c) f (s h) f (s c). Intuitively: to reelect, signal must be more likely under honest than under corrupt incumbent. Under Assumption 1, equivalent to s (h + c)/2. Given candidate equilibrium (h, c) probability of getting reelected as a function of x 1 = x: π(x) = Pr [x + z (h + c)/2] = F [(h + c)/2 x]. 7 / 12

8 Analysis: first period Honest politician does not take a bribe and solves: max W αx 2 + W π(x) (1 µ)α(x c x 2 ) 2 (1 π(x)) Under Assumption 1 this is a convex problem. Denoting reelection motive H = W + (1 µ)α(x2 c)2, FOC gives 2αx H f ((h + c)/2 x) = 0. Corrupt politician jointly maximizes with lobby: max{w αx 2 β(x b) 2 + (W αβ x α + β b2 )π(x) + (1 µ)( αβ α + β b2 B 2 )(1 π(x)) µβb 2 (1 π(x))} Extra reelection incentive: R = (χ + µ µχ)b 2 β 2 /(α + β) 0. Future corruptability and bribe increase reelection incentive. FOC gives 2αx 2β(x b) (H + R) f ((h + c)/2 x) = 0. 8 / 12

9 Equilibrium In equilibrium honest must set x = h and corrupt must set x = c, hence 2αh H f ((h c)/2) = 0 and 2αc 2β(c b) (H + R) f ((h c)/2) = 0. These imply that h < 0 and c < bβ/(α + β). For an honest politician, a move to the left from zero generates: A second order loss in current utility. A first order gain in reelection probability. Prop. 2. There exists a unique PBE in undominated strategies. 1 In the first period choices satisfy h < c and a politician is reelected iff s (h + c)/2. 2 Honest politicians always choose populist policies: h < 0. 3 Corrupt politicians get positive bribes both periods. Uniqueness holds because incentive to separate f ((h c)/2) is stronger when policies are closer. Hence at the margin When Honest moves left, Corrupt wants to move right. When Corrupt moves left, Honest wants to move left. 9 / 12

10 Comparative statics Prop. 3. For W small, corrupt politicians choose c > 0. If W is large and α/β > 4/3, corrupt politicians choose c < 0. When W is small, reelection incentive is smaller, making populist policies too costly. When W is large and β not too large, reelection incentive and hence signalling motive is very strong. Prop. 4. The populist biases p = h and q = c bβ/(α + β) are larger when (1) W is higher; (2) bribing is more efficient; (3) χ is higher. The lower µ the higher p; and the higher q iff χ > χ. Basic logic is that incentives to signal are higher because reelection is more attractive. In first three cases this is due to Higher benefits from office W. More efficient bribing (not included in the slides) increases joint utility of corrupt politician and lobby if reelected. Higher share χ of joint surplus if keeping office. When honest share µ is lower: Successor is more likely to set x2 c, increasing reelection incentive for honest politician. Same effect increases reelection incentive for corrupt politician, but reduces it for lobby. 10 / 12

11 Comparative statics 2 Prop. 5. (1). For W small, an increase in polarization b increases populist bias p. Polarization increases reelection benefits for both types. But makes it more difficult for corrupt politicians to masquerade as honest, reducing the incentive to be populist. When rents from office do not dominate reelection incentives, the first effect is stronger. Prop. 5. (2). An increase in σ 2 decreases populist bias of both types, p and q. With higher noise, choices have a smaller effect on beliefs and elections. Overall, populism is more likely when rents from office are large, politicians are corrupt, bribing is efficient, and society is polarized. The paper also looks at term limits, right-wing populism, and other extensions. 11 / 12

12 2. Game theory in economics Game theory is an actively researched field in microeconomics. For most of us, game theory is primarily a tool in applied economics, commonly used in several fields: Industrial organization; Political economy; Contract theory; Behavioral economics; Macroeconomics. Broader benefits of taking a game theory course: Improves rigorous thinking: difference between what model should and what model does predict. Some experience building and solving models. 12 / 12