nep-gth New Economics Papers
on Game Theory
Issue of 2018‒11‒05
27 papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Does moral play equilibrate? By Bomze, Immanuel; Schachinger, Werner; Weibull, Jorgen
  2. Coordination in Global Games with Heterogeneous Agents By Serrano-Padial, Ricardo
  3. Asymptotic value in frequency-dependent games with separable payoffs: a differential approach By Joseph Abdou; Nikolaos Pnevmatikos
  4. Weighted Committee Games By Kurz, Sascha; Mayer, Alexander; Napel, Stefan
  5. Lock-in through passive connections By Cui, Zhiwei; Weidenholzer, Simon
  6. Sorting in Iterated Incumbency Contests By Nöldeke, Georg; Häfner, Samuel
  7. Court-Appointed Experts and Accuracy in Adversarial Litigation By Chulyoung Kim; Paul S. Koh
  8. k-price auctions and Combination auctions By Martin Mihelich; Yan Shu
  9. An Entry Game with Learning and Market Competition By Chia-Hui Chen; Junichiro Ishida; Arijit Mukherjee
  10. A Comment on "Transparency, Complementarity and Holdout" By Maurya, Amit Kumar
  11. Bargaining order in multilateral bargaining with imperfect compliments By Maurya, Amit Kumar
  12. Globalization and the Concentration of Talent By Schetter, Ulrich; Tejada, Oriol
  13. Fair Cake-Cutting in Practice By Maria Kyropoulou; Josu\'e Ortega; Erel Segal-Halevi
  14. Beyond Grim: Punishment Norms in the Theory of Cooperation By Gabriele Camera; Alessandro Gioffré
  15. Expected Utility Preferences versus Prospect Theory Preferences in Bargaining By Khan, Abhimanyu
  16. Treatment Effect Models with Strategic Interaction in Treatment Decisions By Tadao Hoshino; Takahide Yanagi
  17. A Dynamic Theory of Secession By Joan Esteban; Sabine Flamand; Massimo Morelli; Dominic Rohner
  18. Multilinear Superhedging of Lookback Options By Alex Garivaltis
  19. A Representation Theorem for General Revealed Preference By Mikhail Freer; Cesar Martinelli
  20. Democracy and compliance in public goods games By Gallier, Carlo
  21. Social Image or Social Norm?: Re-examining the Audience Effect in Dictator Game Experiments By Chulyoung Kim; Sang-Hyun Kim
  22. Electives Shopping, Grading Competition, and Grading Norms By Martin Gregor
  23. Trade and Domestic Policies in Models with Monopolistic Competition By Alessia Campolmi; Harald Fadinger; Chiara Forlati
  24. The uncovered set and the core: Cox's (1987) result revisited By Anindya Bhattacharya; Victoria Brosi; Francesco Ciardiello
  25. Taxes, Transfers and Income Distribution in Chile: Incorporating Undistributed Profits By Bernardo Candia; Eduardo Engel
  26. Optimal Education Policy and Human Capital Accumulation in the Context of Brain Drain By Djajic, Slobodan; Docquier, Frédéric; Michael, Michael S.
  27. Prosociality, Political Identity, and Redistribution of Earned Income: Theory and Evidence. By Sanjit Dhami; Emma Manifold; Ali al-Nowaihi

  1. By: Bomze, Immanuel; Schachinger, Werner; Weibull, Jorgen
    Abstract: Some finite and symmetric two-player games have no (pure or mixed) symmetric Nash equilibrium when played by partly morally motivated players. The reason is that the "right thing to do" may be not to randomize. We analyze this issue both under complete information between equally moral players and under incomplete information between arbitrarily moral players. We provide necessary and sufficient conditions for the existence of equilibrium and illustrate the results with examples and counter-examples.
    Keywords: Nash equilibrium, morality, homo moralis, social preferences, incomplete information
    JEL: C72 D01 D64 D82 D91
    Date: 2018–10–16
  2. By: Serrano-Padial, Ricardo (Drexel University)
    Abstract: This paper studies equilibrium selection in large coordination games played by heterogeneous agents, such as models of bank runs, currency attacks or technology adoption. Player payoffs are affected by the average action and the player's type, as well as a global parameter reflecting economic fundamentals. I introduce the notion of ex ante risk dominance and show that it coincides with the global games selection in games with payoffs that are separable in average action and type. Ex ante risk dominance provides an economic interpretation behind the global games selection in terms of maximizing ex ante expected payoffs under pessimistic beliefs. I characterize the ex ante risk dominant equilibrium, pinning down the presence of tipping points in terms of economic fundamentals. I also show that payoff separability is needed for the global games selection to be uniform, that is, to be robust to changes in the distribution of signal noise.
    Keywords: global games; heterogeneity; risk dominance; uniform selection
    JEL: C72 D82 D84
    Date: 2018–10–03
  3. By: Joseph Abdou (Centre d'Economie de la Sorbonne); Nikolaos Pnevmatikos (Université Paris 2 Panthéon-Assas)
    Abstract: We study the asymptotic value of a frequency-dependent zero-sum game with separable payoff following a differential approach. The stage payoffs in such games depend on the current actions and on a linear function of the frequency of actions played so far. We associate to the repeated game, in a natural way, a differential game and although the latter presents an irregularity at the origin, we prove that it has a value. We conclude, using appropriate approximations, that the asymptotic value of the original game exists in both the n-stage and the ?-discounted games ant that it coincides with the value of the continuous time game
    Keywords: stochastic game; frequency dependent payoffs; continuous-time game; Hamilton-Jacobi-Bellman-Isaacs equation
    JEL: C73
    Date: 2016–11
  4. By: Kurz, Sascha; Mayer, Alexander; Napel, Stefan
    Abstract: Players in a committee, council, or electoral college often wield asymmetric numbers of votes. Binary decision environments are then conventionally modeled as weighted voting games. We introduce weighted committee games in order to describe decisions on three or more alternatives in similarly succinct fashion. We compare different voting weight configurations for plurality, Borda, Copeland, and antiplurality rule. The respective geometries and very different numbers of structurally non-equivalent committees have escaped notice so far. They determine voting equilibria, the distribution of power, and other aspects of collective choice.
    Keywords: voting games,weighted voting,geometry of voting,voting power,Borda rule,Copeland rule,plurality,antiplurality
    JEL: C71 D71 C63
    Date: 2018
  5. By: Cui, Zhiwei; Weidenholzer, Simon
    Abstract: We consider a model of social coordination and network formation where agents decide on an action in a coordination game and on whom to establish costly links to. We study the role of passive connections; these are connections to a given agent that are supported by other agents. Such passive connections may inhibit agents from switching actions and links, as this may result in a loss of payoff received through them. When agents are constrained in the number of links they may support, this endogenously arising form of lock-in leads to mixed profiles, where different agents choose different actions, being included in the set of Nash equilibria. Depending on the precise parameters of the model, risk- dominant, payoff- dominant, or mixed profiles are stochastically stable. Thus, agents’ welfare may be lower as compared to the case where payoff is only received through active links. The network formed by agents plays a crucial role for the propagation of actions, it allows for a contagious spread of risk dominant actions and evolves as agents change their links and actions.
    Date: 2018–10–22
  6. By: Nöldeke, Georg; Häfner, Samuel
    Abstract: This paper analyzes incumbency contests in a large population setting. Incumbents repeatedly face different challengers, holding on to their positions until defeated in a contest. Defeated incumbents turn into challengers until they win a contest against an incumbent, thereby regaining an incumbency position. Individuals are heterogeneous as regards their payoffs from being incumbent. We consider steady-state equilibria and study how and to which extent individuals sort into the incumbency positions depending on their type. In particular, we identify sufficient conditions for positive sorting, meaning that types with higher incumbency payoffs are overrepresented among the incumbents, and show that negative rather than positive sorting may also arise in equilibrium when these conditions are violated. Further results show how incumbency rents, surplus, and sorting are affected by the frequency at which incumbency is contested.
    Keywords: Contests,Sorting,Incumbency Rents,Steady-State Equilibrium
    JEL: C72 D72 D74
    Date: 2018
  7. By: Chulyoung Kim (Yonsei University); Paul S. Koh (Columbia University)
    Abstract: Concerned about evidence distortion arising due to litigants' strong incentive to misrep- resent information provided to fact-finders, legal scholars and commentators have long suggested that courts appoint their own advisors for neutral information regarding dis- putes. This paper examines the litigants' problem of losing incentive to provide informa- tion when judges seek the advice of court-appointed experts. Within a standard litigation game framework, we find that assigning court-appointed experts involves a trade-off: al- though such experts help judges obtain more information overall, thereby reducing the number of errors during trials, they weaken litigants' incentive to supply expert informa- tion, thus undermining the adversarial nature of the current American legal system.
    Keywords: litigation game; court-appointed expert; persuasion game; evidence distortion.
    JEL: C72 D82 K41
    Date: 2018–10
  8. By: Martin Mihelich; Yan Shu
    Abstract: We provide an exact analytical solution of the Nash equilibrium for $k$- price auctions. We also introduce a new type of auction and demonstrate that it has fair solutions other than the second price auctions, therefore paving the way for replacing second price auctions.
    Date: 2018–09
  9. By: Chia-Hui Chen; Junichiro Ishida; Arijit Mukherjee
    Abstract: This paper provides a dynamic game of market entry to illustrate entry dynamics in an uncertain market environment. Our model features both private learning about the market condition and market competition, which give rise to the first-mover and second-mover advantages in a unified framework. We characterize symmetric Markov perfect equilibria and identify a necessary and sufficient condition for the first-mover advantage to dominate, which elucidates when and under what conditions a firm becomes a pioneer, an early follower or a late entrant. We also derive equilibrium payoff bounds to show that pioneering entry is generally payoff-enhancing, even though it is driven by preemption motives, and discuss efficiency properties of entry dynamics.
    Date: 2018–10
  10. By: Maurya, Amit Kumar
    Abstract: The paper is a comment on "Transparency, Complementarity and Holdout" by Roy Chowdhury and Sengupta(2012). They analyse a model of multilateral bargaining under the assumption of common discount factor. We show a strong drawback of employing such an assumption.
    Keywords: Multilateral bargaining, discount factors
    JEL: C72 C78
    Date: 2018–10–15
  11. By: Maurya, Amit Kumar
    Abstract: Using a sequential model of multilateral bargaining involving one buyer and two sellers, who are selling objects which are imperfect compliments for the buyer, we analyse buyer’s preferred bargaining order i.e. whether the buyer prefers to buy higher valuation object first or second. For a narrow range of parameters, where players are patient enough and objects exhibit high degree of complimentarity, multiple equilibria exist such that both the bargaining orders are preferred. For rest of the range, which is relatively much larger, buyer prefers to buy higher valuation object first.
    Keywords: Key words: Multilateral bargaining; Bargaining order; Imperfect compliments
    JEL: C72 C78
    Date: 2018–10–18
  12. By: Schetter, Ulrich; Tejada, Oriol
    Abstract: We analyze the allocation of talent across teams in large matching markets with competition for rank. We show that under general conditions globalization in the form of a convex transformation of payoffs promotes the concentration of talent, i.e. it makes positive assortative matching more likely and negative assortative matching less likely. This is in line with recent trends in European football (soccer) leagues.
    Keywords: globalization,inequality,matching,rank competition,strategic interaction
    JEL: D00 D02 D3 D4 D62 D85 J01 P40
    Date: 2018
  13. By: Maria Kyropoulou; Josu\'e Ortega; Erel Segal-Halevi
    Abstract: Using a lab experiment, we investigate the real-life performance of envy-free and proportional cake-cutting procedures with respect to fairness and preference manipulation. We find that envy-free procedures, in particular Selfridge-Conway and the symmetric and asymmetric versions of cut-and-choose, are fairer and also are perceived as fairer than their proportional counterparts, despite the fact that agents very often manipulate them. Our results support the practical use of these procedures, and more generally, of envy-free cake-cutting mechanisms. We also find that subjects learn their opponents' preferences after repeated interaction and use this knowledge to improve their allocated share of the cake. Learning reduces truth-telling behavior and envy.
    Date: 2018–10
  14. By: Gabriele Camera; Alessandro Gioffré
    Abstract: The theory of repeated games asserts that, when past conduct is unobservable, patient individuals can attain the efficient outcome if cooperators suffer large losses to defectors, and react by forever defecting. This extreme "grim" punishment is, in fact, counterproductive when losses are small, as it prevents cooperation among patient players. Here we show how to resolve this non-existence problem. A class of moderate punishments exists, which support full cooperation independent of the size of losses to defectors. Our theory provides a rationale for the empirical observation that grim punishment is uncommon in laboratory studies of cooperation.
    Keywords: prisoner’s dilemma, random matching, social norms.
    JEL: E4 E5 C7
    Date: 2018
  15. By: Khan, Abhimanyu
    Abstract: Are individuals always better off when their preferences can be represented by expected utility? I study this question in a bargaining game where individuals bargain over a pie of fixed size, and I contrast the share received in the long-run by expected utility maximisers with the share they would receive if their preferences were described by prospect theory preferences instead when, in either case, they bargain with expected utility maximisers. I present a necessary and sufficient condition for individuals to obtain a higher share of the pie if their preferences obey prospect theory rather than expected utility. I decompose the effect that the three features that characterise prospect theory preferences -- reference point dependence, loss-aversion and probability weighting -- have on the bargaining outcome, and show that loss-aversion does not have any effect on the outcome of the bargaining process, reference-point dependent preference confers an unambiguous advantage and probability weighting is unambiguously disadvantageous. This ties in with the main result outlined earlier: if the upward pull of reference point dependence is relatively stronger than the downward push of probability weighting, then individuals are better off with prospect theory preferences than with expected utility preferences, and vice-versa.
    Keywords: bargaining, expected utility prospect theory, reference point dependence, loss aversion, probability weighting
    JEL: C73 C78 D01 D81 D83
    Date: 2018–10–06
  16. By: Tadao Hoshino; Takahide Yanagi
    Abstract: This study develops identification and estimation methods for treatment effect models with strategic interaction in treatment decisions. We consider models where one's treatment choice and outcome can be endogenously affected by others' treatment choices. We formulate the interaction of treatment decisions as a two-player complete information game with potential multiple equilibria. For this model, under the assumption of a stochastic equilibrium selection rule, we prove that the marginal treatment effect (MTE) from one's own treatment and that from his/her partner's can be separately point-identified using a latent index framework. Based on our constructive identification results, we propose a two-step semiparametric procedure for estimating the MTE parameters using series approximation. We show that the proposed estimator is uniformly consistent with the optimal convergence rate and has asymptotic normality.
    Date: 2018–10
  17. By: Joan Esteban; Sabine Flamand; Massimo Morelli; Dominic Rohner
    Abstract: This paper builds a dynamic theory of secessions, conflictual or peaceful, analyzing the forward looking interaction between groups in a country. The proposed framework allows us to jointly address several key stylized facts on secession, and generates several novel predictions. We find that if a group out of power is small enough, then the group in power can always maintain peace with an acceptable offer of surplus sharing for every period, while when there is a mismatch between the relative size and the relative surplus contribution of the minority group, conflict followed by secession can occur. Accepted peaceful secession is predicted for large groups of similar prosperity, and higher patience is associated to a higher chance of secession. We formulate as a result a number of policy recommendations on various dimensions of federalism and other institutions.
    Keywords: secessions, conflict, surplus sharing, mismatch
    JEL: C70 D74
    Date: 2018
  18. By: Alex Garivaltis
    Abstract: In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel $W_\theta(X)/D(X)$, where $W_\theta(X)$ is the trader's final wealth and $D(X)$ is the final wealth that would have accrued to a $\$1$ deposit into the best constant-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. The resulting "universal portfolio" compounds its money at the same asymptotic rate as the best rebalancing rule in hindsight, thereby beating the market asymptotically under extremely general conditions. Smitten with this (1998) result, the present paper solves the most general tractable version of Cover and Ordentlich's (1998) max-min game. This obtains for performance benchmarks (read: derivatives) that are separately convex and homogeneous in each period's gross-return vector. For completely arbitrary (even non-measurable) performance benchmarks, we show how the axiom of choice can be used to "find" an exact maximin strategy for the trader.
    Date: 2018–10
  19. By: Mikhail Freer; Cesar Martinelli
    Abstract: We provide a representation theorem for revealed preference of an agent whose consumption set is contained in a general topological space (separable Hausdorff space). We use this result to construct a revealed preference test that applies to choice over infinite consumption streams and probability distribution spaces, among other cases of interest in economics. In particular, we construct a revealed preference test for best-responding behavior in strategic games.
    Keywords: Revealed preference, representation theorem, preference extensions, equilibrium
    Date: 2018–10
  20. By: Gallier, Carlo
    Abstract: I investigate if, how, and why the effect of a contribution rule in a public goods game depends on how it is implemented: endogenously chosen or externally imposed. The rule prescribes full contributions to the public good backed by a nondeterrent sanction for those who do not comply. My experimental design allows me to disentangle to what extent the effect of the contribution rule under democracy is driven by self-selection of treatments, information transmitted via the outcome of the referendum, and democracy per se. In case treatments are endogenously chosen via a democratic decision-making process, the contribution rule significantly increases contributions to the public good. However, democratic participation does not affect participants’ contribution behavior directly, after controlling for self-selection of treatments and the information transmitted by voting.
    Keywords: Laboratory experiment,public good,democracy,endogenous institutions,voting,contribution rule,compliance
    JEL: C91 D02 D72 K42
    Date: 2018
  21. By: Chulyoung Kim (Yonsei University); Sang-Hyun Kim (Yonsei University)
    Abstract: Andreoni and Bernheim (2009) considers a variant of the dictator game in which an exogenous force, called "nature", overturns the dictator's decision with some known probability. They find that as the likelihood of nature's intervention increased, more subjects mimicked the nature's move. We replicate their experiment, and examine a new treatment in which the dictator's decision is revealed to the recipient even when the dictator mimics nature's move. We find that (i) many dictators' decisions were affected by nature's intervention even when their choice was observed by the recipient, which suggests that the intervention altered not only the incentive to signal one's fair-mindedness but also the perception of appropriate action, but (ii) still dictators' behavior under the two treatments differed significantly, which suggests that the audience effect also matters greatly in AB's and our experiments.
    Keywords: Social image, Social norm, Dictator game, Altruism
    Date: 2018–10
  22. By: Martin Gregor (Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Smetanovo nabrezi 6, 111 01 Prague 1, Czech Republic)
    Abstract: This paper analyzes grading competition between instructors of elective courses when students shop for high course scores, the instructors maximize class size, and the school imposes a ceiling on mean course scores to limit grade inflation. Under this grading norm, we demonstrate that curriculum flexibility (more listed courses or less required courses) intensifies the competition: in particular, both top and mean realized scores increase. To tame incentives to provide excessively large scores, we suppose that the school additionally introduces a top-score grading norm. We consider three scenarios. First, the school caps top scores directly. Then, grading competition divides students into a concentrated group of achievers and a dispersed group of laggards. Second, the school normalizes the range of scores by changing the mean-score ceiling. Upon normalization, scores of a less flexible curriculum first-order stochastically dominate scores of a more flexible curriculum. Hence, all students will prefer rigid curricula. Third, the school requires that the mean-score ceiling is evaluated for enrolled students instead of all students. Then, the instructors stop competing for students which introduces sorting inefficiencies. Overall, we show that addressing grade inflation through grading norms may generate inequalities, rigidities, and inefficiencies.
    Keywords: grading competition, grades compression, grading norms, Continuous Lotto games, Captain Lotto games, higher education
    JEL: C72 D02 D21 I21 I23
    Date: 2018–10
  23. By: Alessia Campolmi; Harald Fadinger; Chiara Forlati
    Abstract: We consider unilateral and strategic trade and domestic policies in single and multi-sector versions of models with CES preferences and monopolistic competition featuring homogeneous (Krugman, 1980) or heterogeneous firms (Melitz, 2003). We first solve the world-planner problem to identify the efficiency wedges between the planner and the market allocation. We then derive a common welfare decomposition in terms of macro variables that incorporates all general-equilibrium eects of trade and domestic policies and decomposes them into consumption and production-eciency wedges and terms-of-trade effects. We show that the Nash equilibrium when both domestic and trade policies are available is characterized by first-best-level labor subsidies that achieve production efficiency, and inefficient import subsidies and export taxes that aim at improving domestic terms of trade. Since the terms-of-trade externality is the only beggar-thy-neighbor motive, it remains the only reason for signing trade agreements in this general class of models. Finally, we show that when trade agreements only limit the strategic use of trade taxes but do not require coordination of domestic policies, the latter are set inefficiently in the Nash equilibrium in order to manipulate the terms of trade.
    Keywords: Heterogeneous Firms, Trade Policy, Domestic Policy, Trade Agreements, Terms of Trade, Efficiency, Tariffs and Subsidies
    JEL: F12 F13 F42
    Date: 2018–10
  24. By: Anindya Bhattacharya; Victoria Brosi; Francesco Ciardiello
    Abstract: In this work first it is shown that in contradiction to the well-known claim in Cox (1987) (repeated in a number of subsequent works), the uncovered set in a multidimensional spatial voting situation (under the usual regularity conditions) does not necessarily coincide with the core even when the core is singleton: in particular, the posited coincidence result, while true for an odd number of voters, may cease to be true when the number of voters is even. Then we provide a characterization result for the case with even number of voters: a singleton core is the uncovered set in this case if and only if the unique element in the core is the Condorcet winner.
    Keywords: Spatial Voting Games; Uncovered set; Core; Stable Set.
    JEL: D71 C71
    Date: 2018–10
  25. By: Bernardo Candia (Universidad de Chile); Eduardo Engel (Universidad de Chile)
    Abstract: This paper seeks to measure the distributive impact of fiscal interventions in Chile, applying the “Commitment to Equity†(CEQ) methodology, a standardized fiscal incidence analysis. As a methodological innovation, we incorporated income accrued and not received by Chilean taxpayers through their companies and corporations into the distribution of pre-fiscal income. We find that the difference between the distribution of accrued and received income turns out to be important, around 6 Gini percentage points for each main concept of income. In addition, when moving from the distribution of market income to the distribution of final income (after taxes and transfers) the distribution of income improves by 7 Gini percentage points. To assign the improvement in the distribution of income between the different fiscal interventions, we apply the Shapley value and it is observed that half of the improvement in the distribution of income is due to transfers in education, while direct taxes only explain 20% of the reduction of the Gini coefficient. Finally, based on the simulation of the impact of the 2014 tax reform carried out by the World Bank, we estimate that the reform would produce an additional reduction of 2.4 Gini percentage points when going from market income to final income.
    Keywords: Fiscal incidence, inequality, poverty, undistributed profits, taxes, transfers, Chile
    JEL: D31 H22
    Date: 2018–09
  26. By: Djajic, Slobodan (Graduate Institute of International and Development Studies, Geneva); Docquier, Frédéric (Université catholique de Louvain); Michael, Michael S. (University of Cyprus)
    Abstract: This paper revisits the question of how brain drain affects the optimal education policy of a developing economy. Our framework of analysis highlights the complementarity between public spending on education and students' efforts to acquire human capital in response to career opportunities at home and abroad. Given this complementarity, we find that brain drain has conflicting effects on the optimal provision of public education. A positive response is called for when the international earning differential with destination countries is large, and when the emigration rate is relatively low. In contrast with the findings in the existing literature, our numerical experiments show that these required conditions are in fact present in a large number of developing countries; they are equivalent to those under which an increase in emigration induces a net brain gain. As a further contribution, we study the interaction between the optimal immigration policy of the host country and education policy of the source country in a game-theoretic framework.
    Keywords: migration of skilled workers, immigration policy, education policy
    JEL: F22 J24 O15
    Date: 2018–09
  27. By: Sanjit Dhami; Emma Manifold; Ali al-Nowaihi
    Abstract: We explore the relation between social political identity and prosociality. We first construct a theoretical model to generate predictions for the behavior of players in an ultimatum game who are influenced by social political identity. Then we use a novel subject pool-registered members of British political parties - to play the ultimatum game, and test our predictions. Incomes can either be unearned and untaxed (Treatment 1) or earned, taxed, and redistributed (Treatment 2). We find that the choices of the proposers and the responders are consistent with social identity theory (higher offers and lower minimum acceptable offers to ingroup members) although proposers show quantitatively stronger social identity effects. Moving from Treatment 1 to Treatment 2, offers by proposers decline and the minimum acceptable offers by responders (both as a proportion of income) also decline by almost the same amount, suggesting shared understanding that is characteristic of social norms.
    Keywords: social identity, prosocial behavior, ultimatum game, fiscal redistribution, entitlements
    JEL: D01 D03
    Date: 2018

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