The Scope of Cooperation: Values and Incentives

Transcription

1 The Scope of Cooperation: Values and Incentives Guido Tabellini presented by Armando Miano and Giorgio Monti IGIER VSI - 21st March 2014 Guido Tabellini The Scope of Cooperation: Values and Incentives 1 / 40

2 Outline 1 Introduction 2 Exogenous Values Discussion 3 Endogenous Values Discussion 4 Endogenous Enforcement The enforcement Regime in Political Equilibrium Equilibrium Dynamics 5 Conclusions Guido Tabellini The Scope of Cooperation: Values and Incentives 2 / 40

3 Introduction What this paper wants to answer Why and in which situations individuals cooperate? Traditional economists approach: Axelrod (1984), Gambetta (1988), Dixit (2004) Reputation Incentives Temptation to cheat One important dimension is missed: Individuals internalize norms of good conduct Guido Tabellini The Scope of Cooperation: Values and Incentives 3 / 40

4 Introduction What this paper wants to answer Norms of Good Conduct Origin Application Persistence in dierent environments Evolution over time Interaction with: Economic environment Political environment Economics: Individual preferences as exogenous variable Guido Tabellini The Scope of Cooperation: Values and Incentives 4 / 40

5 Introduction Object of this paper Combining ideas from economics and sociology Cooperation as resulting from a trade-o between: 1 Material Incentives 2 Individual Values How individual values that sustain cooperation evolve endogenously over time? Guido Tabellini The Scope of Cooperation: Values and Incentives 5 / 40

6 Introduction Diusion of Values Depends on: Legal Institutions Political environment Localized economic activity vs Globalization Limited Morality vs Generalized Morality Baneld (1958), Platteau (2004) Limited morality: cooperation with a narrow circle of friend of relatives, frequent cheating with others Generalized morality: respect for abstract individuals and their rights, cooperation over a large range of situations Guido Tabellini The Scope of Cooperation: Values and Incentives 6 / 40

7 Introduction Persistence of Institutional Outcome Through the diusion of values from parents to kids, the initial environment determines the steady state outcome: Limited morality Low legal enforcement, poor values, lack of cooperation Generalized morality Well-functioning legal institutions, high values, strong cooperation These results can explain the puzzling persistence of institutional outcomes emphasized by Acemoglu, Johnson and Robinson (2001), Glaesen et al. (2004), Acemoglu and Robinson (2006), Putnam (1993), Guiso, Sapienza and Zingales (2008). Guido Tabellini The Scope of Cooperation: Values and Incentives 7 / 40

8 Exogenous Values Dixit Model (2004) Matching between 2 traders 2 periods Localization of information: Reputation matters Normal vs Machiavellian Players Guido Tabellini The Scope of Cooperation: Values and Incentives 8 / 40

9 Exogenous Values Our Model One-period-lived individuals uniformly distributed on the circumference of size 2S Max. distance between two individuals: S g(y) > 0: random probability of matching another individual at a distance y Guido Tabellini The Scope of Cooperation: Values and Incentives 9 / 40

10 Exogenous Values The Game The two matched individuals observe their distance and play a prisoner's dilemma game: Each player simultaneously chooses whether to cooperate (C ) or not to cooperate (NC ) Assumptions: c > h l, w > 0 l w Guido Tabellini The Scope of Cooperation: Values and Incentives 10 / 40

11 Exogenous Values The Noneconomic (psychological) Benet Besides the playos of the prisoner's dilemma game, each individuals enjoys a noneconomical benet d, whenever it plays C, which has the following features: 1 d > max(l, w) 2 d decays with distance at an exponential rate θ > 0 3 d(y) = de θy This formulation captures two plausible ideas: Individuals are motivated by more than just material payo These norms of good conduct apply with more force with more familiar individuals Guido Tabellini The Scope of Cooperation: Values and Incentives 11 / 40

12 Exogenous Values The Players Only two types of players: k = 0 : Bad Player, not trustworthy k = 1 : Good Player Same benet d of cooperating θ 0 > θ 1 Individuals observe distance y, but not the type k of the opponent player In this basic model the fraction of good (k = 1) types in the population is the same at any point in the circle, and it is a xed parameter n, with 1 > n > 0 Guido Tabellini The Scope of Cooperation: Values and Incentives 12 / 40

13 Exogenous Values The Equilibrium We denote π(y) the probability that the opponent at a distance y will play C Player's expected material gain from playing NC rather than C: T (π(y)) = [l π(y)(l w)] > 0 (1) This expression captures the temptation not to cooperate ad it is always positive. Given that l w, the function T(π(y)) is non-increasing in π(y): strategic complementarity The temptation is the same for all players: it must be balanced against the non economic benet of cooperation de θy Guido Tabellini The Scope of Cooperation: Values and Incentives 13 / 40

14 Exogenous Values The Equilibrium A type k = 0, 1 is indierent from playing C or NC in a match with a player at distance y k if: T (π(ỹ k )) = de θk ỹ k (2) Solving for y k, we obtain: ỹ k = {ln d ln[(w l)π(ỹ k ) + l]}/θ k (3) Holding π constant, this individual plays C in a match with someone at distance y < ỹ k plays NC in a match with someone at distance y > ỹ k Guido Tabellini The Scope of Cooperation: Values and Incentives 14 / 40

15 Exogenous Values The Equilibrium Consider a bad player k = 0 and suppose π(y)=1, Then (3) reduces to : What about a good player, k = 1? Up to distance y Y 0 a good player also plays C Y 0 = [ln d ln w]/θ 0 (4) For distance y > Y 0 the good player realizes that all bad players will play NC, and his most optimistic expectation is that his/her opponent cooperates only if he/she is good, which happens with probability n. Hence we can put π(y) = n in the r.h.s. of (3): ỹ 1 = [ln d ln[(w l)n + l]]/θ 1 (5) Guido Tabellini The Scope of Cooperation: Values and Incentives 15 / 40

16 Exogenous Values The Equilibrium In equilibrium the upper threshold of cooperation for a good player is: Y 1 = max{ỹ 1, Y 0 } (6) Note that Y 1 Y 0, with strict inequality if n is suciently large, or if the two types are suciently dierent from each other. In particular Y 1 > Y 0 even at n = 0 if the following condition is satised: θ 0 θ > ln(l/d) 1 ln(w/d) Because l w this condition implies θ 0 θ 1 Finally if l = w the r.h.s of (3) does not depend on π(.) and the equilibrium is unique Guido Tabellini The Scope of Cooperation: Values and Incentives 16 / 40

17 Exogenous Values Discussion What this basic model says Cooperation is easier to sustain in closer matches Alesina and La Ferrara (2000, 2002) Larger S Less Frequent Cooperation The variable Y 0 may be seen as a small familiar group Y 0^ if: w, θ 0 _ or d ^ Y 1 : Scope of maximal sustainable cooperation Y 1^ also if: l _, or n ^ if l > w (strategic complementarity) Guido Tabellini The Scope of Cooperation: Values and Incentives 17 / 40

18 Endogenous Values Endogenous Values: Individual's type reects two forces: Parents: exogenous inuence of nature or external environment deliberate rational eorts of parents through education. altruistic and care about utility of their children evaluate kid's expected welfare with their own preferences, i.e., Imperfect Empathy assumption (Bisin and Verdier [2001]) An ongoing economy that lasts forever. Individuals live two periods. First period: they are educated by their parents and, once education is completed, they play the game Second period: each individual is the parent of a single kid and his only activity is to devote eort to educating his kid Guido Tabellini The Scope of Cooperation: Values and Incentives 18 / 40

19 Endogenous Values Education increases the probability that the kid becomes good: P(θ k = θ 1 ) = δ + f where f 0 denotes parental eort. However, it is costly for the parent. We assume a quadratic cost function (1/2ϕ)f 2 where ϕ 0 is a parameter that captures the rate at which the marginal cost increases with eort. Once parents have completed the education, each player observes his/her own type and plays the matching game How parents choose the level of education for their children? Guido Tabellini The Scope of Cooperation: Values and Incentives 19 / 40

20 Endogenous Values The Parents' Optimization Problem Let Vt pk denote the parent's evaluation of his/her kid's overall expected utility in the equilibrium of the matching game. V pk t = U k t + d Y k ˆ t 0 e θpz g(z)dz (7) where: Ut k = U(θ k, n t ) is the expected equilibrium material payos of a kid of type k in a game with a fraction n t of good players. d Yt k e θpz g(z)dz is the parent's evaluation of his/her kid's expected 0 noneconomic benet of cooperating in matches of distance smaller than Yt k. θ p is the parent's value parameter, with p = {0, 1}, Yt k is that of the kid. V k t = Vt pk if θ p = θ k Guido Tabellini The Scope of Cooperation: Values and Incentives 20 / 40

21 Endogenous Values The Parents' Optimization Problem Why should parents impose their own values in the evaluation of their kids' welfare rather than using the kids' preferences? It wouldn't have been very plausible if the evaluation had been limited only to alternative material pay-os. Instead in (7) parents express a value judgment on their kids' actions and values reect deeply held convictions about religious or moral principles or belief about long-run consequences of actions. Hence parents are likely to be convinced that what is right for themselves is also right for everyone else and in particular for their kids. Guido Tabellini The Scope of Cooperation: Values and Incentives 21 / 40

22 Endogenous Values The Parents' Optimization Problem Theorem If k p, then V pp V pk with strict inequality if Y 1 > Y 0, i.e., a parent t t always prefers to have a kid with his/her own values. This result reect two assumptions: individual types are not observable and hence there is no incentive for strategic delegation the only reason to change one's kid's value θ k is to induce the kid to change her/his behavior (Y k t ) Corollary A good parent (p = 1) exerts strictly positive eort. A bad parent (p = 0) exerts no eort. Guido Tabellini The Scope of Cooperation: Values and Incentives 22 / 40

23 Endogenous Values The Parents' Trade-o Now, consider the optimal choice of eort of the good parent. At an interior point of optimum the rst-order optimality condition equates the marginal cost and the expected net marginal benet of eort. f t /ϕ = (U 1 t U 0 t ) + d Y 1 ˆ t In choosing their level of eort, parents face a trade-o: Y 0 θ e 1z g(z)dz (8) Increasing their kid trustworthiness hurts the kids expected material payo. The rst term on the RHS is always negative. But a good kid also provides expected direct noneconomic benets to the parent by extending his cooperative behavior to a larger range of matches. The second term on the RHS is always positive. Guido Tabellini The Scope of Cooperation: Values and Incentives 23 / 40

24 Endogenous Values The Parent's Trade-o By Corollary 3, for good parents the benets exceed the costs and hence f t > 0. The parent optimality condition (8) yields to: = ϕd f t = F (Yt 1 ) = ϕd[ e θ1 Yt 1 Y 1 ˆ t g(z)dz + Y 0 { e θ1 Yt 1 + E[e θ1y Yt 1 y Y 0 ] Y 1 ˆ t Y 0 } θ e 1z g(z)dz] Pr(Y 1 t y Y 0 ) (9) It can be proved that the function F (Y 1 t ) is strictly increasing in Y 1 t. Intuitively if the dierence in behavior between good and bad players increases, then good parents are induced to put in more eort to increase the probability of having a good kid. Guido Tabellini The Scope of Cooperation: Values and Incentives 24 / 40

25 Endogenous Values The Parent's Trade-o This property gives rise to strategic complementarity among parents: If parents expect others to put more eort into education, they anticipate that the fraction of good players will increase, expanding the scope of cooperation Yt 1, and they exert more eort. The Educational game is Supermodular Finally the fraction of good players in period t evolves endogenously over time according to n t = n t 1 (δ + f t ) + (1 n t 1 )δ = δ + n t 1 f t (10) where n t 1 denotes the fraction of good parents and f t denotes their eort. Guido Tabellini The Scope of Cooperation: Values and Incentives 25 / 40

26 Endogenous Values The Equilibrium The equilibrium is given by the vector (Yt 1, nt ) that solves the equations: Y 1 t = [lnd ln[(w l)n t + l]]/θ 1 Y (n t ) (11) n t = δ + n t 1 F (Y 1 t ) N(Y 1 t, n t 1 ) (12) Setting n t = n t 1 = n s we obtain the steady state equilibrium. Y 1 s = Y (n s ) (13) n s = δ 1 F (Y 1 s ) (14) Guido Tabellini The Scope of Cooperation: Values and Incentives 26 / 40

27 Endogenous Values Multiplicity of Equilibria If l > w both curves are upward sloping, multiple equilibria are possible. That is, the same n t 1 might imply more that one equilibrium pair and this reects the complementarity between values and cooperation in both strategic interactions. The equilibrium is unique if the curve n t always intersect the curve Yt 1 left to right. A sucient condition for this to happen is: 1 ϕ > l w which says that the marginal cost of eort, 1/ϕ,rises suciently rapidly relative to the stategic complementarity captured by (l w). From now on we will assume that this condition holds. from Guido Tabellini The Scope of Cooperation: Values and Incentives 27 / 40

28 Endogenous Values Unique Equilibrium Guido Tabellini The Scope of Cooperation: Values and Incentives 28 / 40

29 Endogenous Values Discussion Discussion Many phenomena may aect the equilibrium outcome through changes in the underlying parameters. We consider in particular variations in: 1 Level of (exogenous) external enforcement 2 Economic Geography Localization Globalization Guido Tabellini The Scope of Cooperation: Values and Incentives 29 / 40

30 Endogenous Values Discussion External Enforcement The degree to which cooperation is enforced by external institutions inuences the payo of the prisoner's dilemma game. Let q(y) be the probability that cheating goes underdetected, and (1 q(y)) the probability that cheating is discovered and playing NC yields only c, whereas playing C yields h. Better enforcement correspond to a low q(y). Suppose that q(y) = q 0 for matches of distance y y and q(y) = q 1 if y > y, where y Y 0 but near to it. Guido Tabellini The Scope of Cooperation: Values and Incentives 30 / 40

31 Endogenous Values Discussion External Enforcement What are the eect of changes in q 1 and q 0? Better Enforcement in Distant Matches In period 0, q 1 _: curve Y 1 t shifts to the right, curve N(Y 1 t, n t 1 ) unaected, Y 1 0 ^, f 0^, n 0^ In period 1, curve n t shifts upward, Y1 1^ and Y 1 1 > Y 0 1 In the new steady state: higher ns and larger Y 1 s Better Local Enforcement In period 0, q 0 _: Y 0^, f 0 _, the curve n t shifts downward and Y 1 _ In the new steady state: lower ns and larger Y 1 s Guido Tabellini The Scope of Cooperation: Values and Incentives 31 / 40

32 Endogenous Values Discussion Economic Geography Consider the eect of the matching technology, captured by the probability g(y). This immediately shifts the curve n t. In particular if the probability of matches in the interval [Y o, Y 1 ] increases uniformly in period 0, f 0^, n 0^ and Y 1 0 ^. In the new steady state n s will be higher and Y 1 s larger. Guido Tabellini The Scope of Cooperation: Values and Incentives 32 / 40

33 Endogenous Values Discussion Localization and Globalization Whatever increases the probability of matches in the interval [Y o, Y 1 ] increases the diusion of values and cooperation. This may result from: Lower degree of localization, i.e, the probably of matches below Y 0 drops Lower degree of globalization, i.e., the probability of very distant matches (above Y 1 ) drops A possible pattern of development: at early stages transactions are mainly local and values and cooperation remain more limited in scope. As development progress impersonal transactions gain relevance and the scope of cooperation increases. But at even more advanced stages, transactions becomes so spread out that the eect on values may be negative. Guido Tabellini The Scope of Cooperation: Values and Incentives 33 / 40

34 Endogenous Enforcement The enforcement Regime in Political Equilibrium Pattern of external enforcement Assumptions: 1 Probability of matching: g(y) = η 2 l = w The equilibrium is unique 3 1 q(y): probability that cheating is detected 4 For matches up to Y 0, q(y) = q 0, which is given 5 For more distant matches: q(y) = q 1 t determined by government policy 6 q 0 q 1 t Q where Q is a xed parameter These assumptions lead to: Y k t = [ln(d/wq k t )]/θ k, k = 0, 1 Guido Tabellini The Scope of Cooperation: Values and Incentives 34 / 40

35 Endogenous Enforcement The enforcement Regime in Political Equilibrium Political Framework Government policy is set under majority rule in each period. Timing of events: 1 Parents choose eort 2 Kids' type is known and kids vote 3 Kids play the matching game What is the policy preferred by the two types? Good Players: qt 1 = q 0 Bad Players: Trade o Strong enforcement regime ^ qt 1 : higher benet of cheating _ qt 1 : higher range of matches over which take advantage Guido Tabellini The Scope of Cooperation: Values and Incentives 35 / 40

36 Endogenous Enforcement The enforcement Regime in Political Equilibrium Political Equilibrium If d is suciently large relative to the material payos of the prisoner's dilemma, then the rst eect prevails at q 0 Hence: Bad players prefer: q 1 t > q 0 It can be proved that from bad-players' view the optimal policy is time invariant: q 1 t = q, q > q 0 In the political equilibrium: If n t > 1/2 the strong enforcement regime prevails: q 1 t = q 0 If n t < 1/2 the weak enforcement regime prevails: q 1 t = q If n t = 1/2 either regime can prevail Guido Tabellini The Scope of Cooperation: Values and Incentives 36 / 40

37 Endogenous Enforcement Equilibrium Dynamics Eects on the Eort f : Eort under strong enforcement f : Eort under weak enforcement It can be proved that: Lemma 1. f = f Δ > 0 with Δ>0 By Lemma 1: If parents expects n t > 1/2, then the steady state fraction of good player is given by: n s = δ 1 f If parents expect n t < 1/2, instead: n s = δ 1 f +Δ Guido Tabellini The Scope of Cooperation: Values and Incentives 37 / 40

38 Endogenous Enforcement Equilibrium Dynamics Who win the elections? Three possible scenarios: 1 n s > 1/2 political equilibrium with strong enforcement 2 n s < 1/2 political equilibrium with weak enforcement 3 n s < 1/2 < n s both equilibria al possible Which enforcement in the third case? We can easily obtain two thresholds: n= 1 2δ 2f N= 1 2δ 2(f Δ) Equilibrium in t; n t 1 < n : Weak Enforcement n t 1 > N : Strong Enforcement N n t 1 n : Both Strong and Weak Enforcement Regimes Guido Tabellini The Scope of Cooperation: Values and Incentives 38 / 40

39 Endogenous Enforcement Equilibrium Dynamics Discussion The model with endogenous enforcement highlights some interesting issue: Eective law enforcement strengthens the incentives to transmit sound values The quality of law enforcement reects policy choices This results can explain dierent phenomena in social sciences: Why some societies remain trapped in their backwardness Benets of better enforcements are negligible in a society where trust and cooperation are too low The model also faces some problems: Voting system and voters behavior Individual values have a direct impact on political ideologies Guido Tabellini The Scope of Cooperation: Values and Incentives 39 / 40

40 Conclusions Conclusions In this paper Tabellini builds a model that shows how values inuence cooperation and how culture evolves in dierent political and institutional environment. He identies family with the main channel of cultural transmission and he explains the persistence of institutions through parents' educational choices. However, the model can be extended to take into account other important elements: 1 Not just one channel of cultural transmission: Educational institutions Media Peers 2 Joint eect of values and reputation 3 Role of signaling Guido Tabellini The Scope of Cooperation: Values and Incentives 40 / 40