
on Game Theory 
By:  Bó, Inácio Guerberoff Lanari; Hakimov, Rustamdjan 
Abstract:  We introduce a new mechanism for matching students to schools or universities, denoted Iterative Deferred Acceptance Mechanism (IDAM), inspired by procedures currently being used to match millions of students to public universities in Brazil and China. Unlike most options available in the literature, IDAM is not a direct mechanism. Instead of requesting from each student a full preference over all colleges, the student is instead repeatedly asked to choose one college among those which would accept her given the current set of students choosing that college. Although the induced sequential game has no dominant strategy, when students simply choose the most preferred college in each period (denoted the straightforward strategy), the matching that is produced is the Student Optimal Stable Matching. Moreover, under imperfect information, students following the straightforward strategy is an Ordinal Perfect Bayesian Equilibrium. Based on data from 2016, we also provide evidence that, due to shortcomings which are absent in the modified version that we propose, the currently used mechanism in Brazil fails to assist the students with reliable information about the universities that they are able to attend, and are subject to manipulation via cutoffs, a new type of strategic behavior that is introduced by this family of iterative mechanisms and observed in the field. 
Keywords:  Market Design,Matching,Iterative Mechanisms,College Admissions 
JEL:  C78 C92 D63 D78 D82 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2016212&r=gth 
By:  Dmitry Levando (National Research University Higher School of Economics) 
Abstract:  The paper defines a family of nested noncooperative simultaneous finite games to study coalition structure formation with intra and intercoalition externalities. The novelties of the paper are: a definition of every games embeds a coalition structure formation mechanism. Every game has two outcomes  an allocation of players over coalitions and a payoff profile for every player. The family is parametrized by a maximum coalition size in every coalition structure (a partition) in a game. For every partition a player has a partitionspecific set of strategies. The mechanism portions a set of strategies of the game (a Cartesian product) into partitionspecific strategy domains, what makes every partition to be itself a noncooperative game with partitionspecific payoffs for every player. Payoffs are assigned separately for every partition and are independent from the mechanism. Every game in the family has an equilibrium in mixed strategies. The equilibrium can generate more than one coalition and encompasses intra and inter group externalities, what makes it different from the Shapley value. Presence of individual payoff allocation makes it different from a strong Nash, coalitionproof equilibrium, and some other equilibrium concepts. The paper demonstrate some applications of the proposed toolkit: for noncooperative fundamentals of cooperation in a coalition, Bayesian game, stochastic games and construction of a noncooperative criterium of coalition structure stability. 
Keywords:  noncooperative Games 
JEL:  C72 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:hig:wpaper:157/ec/2017&r=gth 
By:  Lauren Larrouy (Université Côte d'Azur; GREDEG CNRS); Guilhem Lecouteux (Université Côte d'Azur; GREDEG CNRS) 
Abstract:  We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We show in particular that those beliefs need not be ratifiable, and therefore that rational players can form actiondependent beliefs. 
Keywords:  prior beliefs, mindreading, simulation, actiondependent beliefs, choice under uncertainty 
JEL:  B41 C72 D81 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:gre:wpaper:201701&r=gth 
By:  Schopf, Mark; Voss, Achim 
Abstract:  In this article, we propose a sequential Nash bargaining solution and apply it to a dynamic bargaining game on exhaustibleresource extraction. The government and two agents bargain via the asymmetric Nash bargaining solution. Should the trilateral negotiation fail, the government chooses one agent for a bilateral negotiation. In this negotiation, the disagreement point is to bargain with the other agent. Finally, should this second bilateral negotiation break down, the government chooses the welfare maximizing policy. In our dynamic bargaining game, the environmental organization is willing to pay for less extraction, because of stockpollution effects, while the extraction firm is willing to pay for extraction per se. The government dislikes extraction, because of flowpollution effects, but is willing to accept some if it is paid for it. It turns out that the disagreement point in the trilateral negotiation is always to bargain with the environmental organization. This is because there is no conflict of interest between the government and the environmental organization concerning extraction. However, as long as stock pollution is still low, it might be optimal for the environmental organization to let this bilateral negotiation break down. We demonstrate how these considerations shape the payments in case of agreement and disagreement, in total and over time. 
JEL:  C71 D72 Q58 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:zbw:vfsc16:145496&r=gth 
By:  Yu Chen (University of Graz) 
Abstract:  We explore the theoretical justification of adopting bilateral mechanism design, which is a simplification of canonical collective mechanism design, in general multiagency contracting games under Bayesian Nash equilibrium. We establish interim payoff equivalence between collective and bilateral mechanism design in the quasiseparable environment, in which inter dependent valuations and correlated types are allowed. We employ interim payooff equivalence to further show the equivalence between optimal bilateral and collective mechanism design, when the principal's payoff exhibits certain relations with separate agents' payoffs. Our analysis can also incorporate individual rationality and budget balance constraints and the asymptotic equivalence. 
Keywords:  Bayesian Nash equilibrium, bilateral mechanism, collective mechanism, interim payoff equivalence, quasiseparable environment 
JEL:  C72 D82 D86 
Date:  2017–02 
URL:  http://d.repec.org/n?u=RePEc:grz:wpaper:201701&r=gth 
By:  Riyanto, Yohanes E.; Roy, Nilanjan 
Abstract:  We report results from experiments designed to investigate the prevalence of turntaking in threeperson finitely repeated threshold public good games without communication. Individuals can each make a discrete contribution. If the number of contributors is at least equal to the threshold, a public benefit accrues to all group members. Players take turns to provide the public good each round when the endowments are homogeneous. When the turntaking path is at odds with efficiency or under private information of endowments, players seldom engage in taking turns. An endogenousmove protocol limits the frequency of miscoordinated outcomes every round. 
Keywords:  Public good provision, Turntaking, Repeated game, Endogenous move, Experiment 
JEL:  C72 C92 D03 D82 H41 
Date:  2017–02–03 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:76565&r=gth 
By:  Reischmann, Andreas 
Abstract:  Many mechanisms have been developed to solve the freerider problem in private public good provision. Most of these mechanisms were designed to have good static (Nash) equilibrium properties. I present in this paper a new class of mechanisms, the Conditional Contribution Mechanisms (CCM), which are designed to have good dynamic equilibrium properties instead. The CCMs give all agents the possibility to condition their contribution on the total level of contribution provided by all agents. Their dynamic incentive structure makes the CCMs particularly suited for repeated public goods. I prove for a very general class of environments that all equilibria of the CCMs under a new variant of Better Response Dynamics, called Unexploitable Better Response Dynamics (UBRD), are Pareto efficient. I further present a first experimental study of one mechanism's performance compared to the performance of the Voluntary Contribution Mechanism. In an environment with binary contribution and linear valuations, agents play the mechanisms in a repeated setting. I test one case of complete information and homogeneous valuations and a second case with incomplete information and heterogeneous valuations. In both cases a significantly higher contribution rate can be observed when the CCM is used. Furthermore, all stable outcomes of the CCM, which are observed in the experiment, are in line with the prediction of UBRD. 
JEL:  H41 D82 C92 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:zbw:vfsc16:145613&r=gth 
By:  Christian Ewerhart 
Abstract:  It is shown that the nplayer lottery contest admits a bestresponse potential (Voorneveld, 2000, Economics Letters). This is true also when the contest technology reflects the possibility of a draw. The result implies, in particular, the existence of a nontrivial example of a strictly competitive game that is bestresponse equivalent to a game with identical payoff functions. 
Keywords:  Potential games, Tullock contest, bestresponse equivalence, zerosum games 
JEL:  C62 C72 D72 
Date:  2017–02 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:242&r=gth 
By:  DECERF, Benoit (Universit e de Namur); VAN DER LINDEN, Martin (Vanderbilt University) 
Abstract:  We introduce a new criterion to compare the properties of mechanisms when the solution concept used induces multiple solutions. Our criterion generalizes previous approaches in the literature. We use our criterion to compare the stability of constrained versions of the Boston (BOS) and deferred acceptance (DA) school choice mechanisms in which students can only rank a subset of the schools they could potentially access. When students play a Nash equilibrium, we show that there is a stability cost to increasing the number of schools students can rank in DA. On the other hand, when students only play undominated strategies, increasing the number of schools students can rank increases stability. We find sim ilar results for BOS. We also compare BOS and DA. Whatever the number of schools students can rank, we find that BOS is more stable than DA in Nash equilibrium, but less stable in undominated strategies. 
Keywords:  Multiple solutions, School choice, Stability, Boston mecha nism, Deferred acceptance mechanism, Nash equilibrium, Undominated strategy 
JEL:  C78 D47 D82 I 
Date:  2016–10–04 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2016033&r=gth 
By:  Warnke, Arne Jonas; Sittl, Roman 
Abstract:  In this paper we consider trends in the distribution of player talent across association football clubs over time. Player talent is the most important prerequisite for team success in professional sports leagues and changes in players' assortativeness in regard to the clubs they play for may arguably be an important factor for changes in competitive balance. We offer a new approach for measuring player talent and its distribution  the partial correlation of each player with the goal margin. We use this measure to analyze the degree of competitive balance over time. This approach enables us to examine how player mobility drives competitive balance over time. Empirical results are based on 19 seasons of the first two divisions of the German Bundesliga as well as domestic cup games. Our results show a decrease in competitive balance over time; better teams tend to attract increasingly better players. We show that this is driven by an increasingly unequal interdivisional distribution of teams, coaches and players, as well as increasing assortativeness in the 1st Bundesliga. We further demonstrate that player transfers between Bundesliga teams results in assortative matching between players and teams. These domestic transfers do not, however, explain the reduction in competitive balance over time. Furthermore, we show that UEFA Champions League payments may have contributed to the reduction in competitive balance over the last two decades. 
JEL:  J44 J63 L83 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:zbw:vfsc16:145838&r=gth 
By:  Srivastava, Vatsalya (Tilburg University, TILEC) 
Abstract:  When players face uncertainty in choosing actions, undesirable outcomes cannot be avoided. Accidental defections caused by uncertainty, that does not depend on the level of care, require a mechanism to reconcile the players. This paper shows the existence of a perfect sorry equilibrium in a game of imperfect public monitoring. In the sorry equilibrium, costly apology is selfimposed in case of accidental defections, making private information public and allowing cooperation to resume. Cost of the apology required to sustain this equilibrium is calculated, the efficiency characteristics of the equilibrium evaluated and outcomes compared to those from other bilateral social governance mechanisms and formal legal systems. It is argued that with the possibility of accidental defections, other social mechanisms have limitations, while formal legal systems can generate perverse incentives. Therefore, apologies can serve as a useful economic governance institution. 
Keywords:  apology; sorry; imperfect public monitoring; uncertainty; social norms; economics governance; Legal institutions; incentives; courts 
JEL:  D8 K4 Z10 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiutil:9340f3b1ebf346b98ffd352d7fa81724&r=gth 
By:  GRANDJEAN, G.; TELLONE, D.; VERGOTE, W. (Université catholique de Louvain, CORE, Belgium) 
Abstract:  We propose a model of network formation in a Tullock contest. Agents first form their partnerships and then choose their investment in the contest. While a link improves the strength of an agent, it also improves the position of her rival. It is thus not obvious that they decide to cooperate. We characterize all pairwise equilibrium networks and find that the network formation process can act as a barrier to entry to the contest. We then analyze the impact of network formation on total surplus and find that a social planner can increase total surplus by creating more asymmetry between agents, as long as this does not reduce the number of participating agents. We show that barriers to entry may either hurt total surplus, as the winner of the prize does not exploit all the possible network benefits, or improve total surplus since less rent is dissipated when competition becomes less fierce. Finally, when networking acts as an endogenous barrier to entry, no pairwise equilibrium network is efficient. 
Keywords:  Network Formation, Tullock Contest, Participation Constraints, Efficiency 
JEL:  D72 D85 
Date:  2016–07–31 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2016032&r=gth 
By:  Wulf Gaertner; Lars Schwettmann; Yongsheng Xu 
Abstract:  We conduct a labexperimental study of bargaining over the distribution of monetary losses. Groups of four differently endowed participants must agree, as a group, on the contribution each participant will make to cover a financial loss imposed on the group. The study sheds light on burden sharing and what loss allocation rules groups adopt. Furthermore, we characterize a new theoretical model which contains the proportional rule and equality of losses as special cases but collides with the constrained equal awards rule. The combination of our model and the constrained equal awards rule can explain the majority of proposals made in our experiment. 
Keywords:  loss sharing, axiomatic characterization of allocation rules, experimental bargaining 
JEL:  C91 D31 D63 D71 
Date:  2017–02 
URL:  http://d.repec.org/n?u=RePEc:exc:wpaper:201701&r=gth 
By:  Drew Fudenberg; Kevin He 
Abstract:  The key issue in selecting between equilibria in signalling games is determining how receivers will interpret deviations from the path of play. We develop a foundation for these offpath beliefs, and an associated equilibrium refinement, in a model where equilibrium arises from nonequilibrium learning by longlived senders and receivers. In our model, nonequilibrium signals are sent by young senders as experiments to learn about receivers' behavior, and different types of senders have different incentives for these various experiments. Using the Gittins index (Gittins, 1979), we characterize which sender types use each signal more often, leading to a constraint we call the "compatibility criterion" on the receiver's offpath beliefs and to the concept of a "typecompatible equilibrium." We compare typecompatible equilibria to signallinggame refinements such as the Intuitive Criterion (Cho and Kreps, 1987) and divine equilibrium (Banks and Sobel, 1987). 
Date:  2017–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1702.01819&r=gth 
By:  Marco Pangallo; James Sanders; Tobias Galla; Doyne Farmer 
Abstract:  Learning would be a convincing method to achieve coordination on a Nash Equilibrium (NE). But does learning converge, and to what? We answer this question in generic 2player, 2strategy games, using ExperienceWeighted Attraction (EWA), which encompasses most extensively studied learning algorithms. We exhaustively characterize the parameter space of EWA learning, for any payoff matrix, and we understand the generic properties that imply convergent or nonconvergent behaviour in 2x2 games. Irrational choice and lack of incentives imply convergence to a mixed strategy in the centre of the strategy simplex, possibly far from the NE. In the opposite limit, in which the players quickly modify their strategies, the behaviour depends on the payoff matrix: (i) a strong discrepancy between the pure strategies describes dominancesolvable games, which show convergence to a unique fixed point close to the NE; (ii) a preference towards profiles of strategies along the main diagonal describes coordination games, with multiple stable fixed points corresponding to the NE; (iii) a cycle of best responses defines discoordination games, which commonly yield limit cycles or lowdimensional chaos. While it is well known that mixed strategy equilibria may be unstable, our approach is novel from several perspectives: we fully analyse EWA and provide explicit thresholds that define the onset of instability; we find an emerging taxonomy of the learning dynamics, without focusing on specific classes of games exante; we show that chaos can occur even in the simplest games; we make a precise theoretical prediction that can be tested against data on experimental learning of discoordination games. 
Date:  2017–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1701.09043&r=gth 
By:  Semyon Malamud (Ecole Polytechnique Federale de Lausanne, Swiss Finance Institute, and Centre for Economic Policy Research (CEPR)); Huaxia Rui (University of Rochester); Andrew B. Whinston (University of Texas at Austin) 
Abstract:  We solve the general problem of optimal risk sharing among a finite number of agents with limited liability. We show that the optimal allocation is characterized by endogenously determined ranks assigned to the participating agents and a hierarchical structure of risk sharing, where all agents take on risks only above the agentspecific thresholds determined by their ranks. When all agents have CARA utilities, linear risk sharing is optimal between two adjacent thresholds. We use our general characterization of optimal risk sharing with limited liability to solve the problem of optimal insurance design with multiple insurers. We show that the optimal thresholds, or deductibles, can be efficiently calculated through the fixed point of a contraction mapping. We then use this contraction mapping technique to derive a number of comparative statics results for optimal insurance design and its dependence on microeconomic characteristics. 
Keywords:  optimal risk sharing, limited liability, optimal insurance design 
JEL:  A10 D86 G22 
URL:  http://d.repec.org/n?u=RePEc:chf:rpseri:rp1205&r=gth 
By:  Batabyal, Amitrajeet 
Abstract:  In this note we use a static game model to analyze the optimal cleanup of an apartment that is shared by two college students. Both students dislike cleaning. However, they also prefer a clean apartment to a dirty one. Student i's utility function embodies the idea that the more time one student spends cleaning, the less valuable is the time spent cleaning by the other student. In this setting, we first determine the best response function of each student (player) i where i=1,2. Second, we determine the cleaning time choices that survive one round of the iterated elimination of strictly dominated strategies (IESDS). Finally, we ascertain the cleaning time choices that survive all rounds of IESDS. 
Keywords:  Apartment, Cleanup, College Student, Static Game, Strictly Dominated Strategy 
JEL:  D01 J22 
Date:  2017–01–07 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:76663&r=gth 
By:  Kanoria, Yash (Columbia University); Saban, Daniela (Stanford University); Sethuraman, Jay (Columbia University) 
Abstract:  We consider a twosided assignment market with agent types and a stochastic structure, similar to models used in empirical studies. We characterize the size of the core in such markets. Each agent has a randomly drawn productivity with respect to each type of agent on the other side. The value generated from a match between a pair of agents is the sum of the two productivity terms, each of which depends only on the type (but not the identity) of one of the agents, and a third deterministic term driven by the pair of types. We prove, under reasonable assumptions, that keeping the number of agent types fixed, the relative size of the core vanishes rapidly as the number of agents grows. Numerical experiments confirm that the core is typically small. Our results provide justification for the typical assumption of a unique core outcome in such markets, that is close to a limit point. Further, our results suggest that, given market composition, the wages are almost uniquely determined in equilibrium. 
Date:  2016–09 
URL:  http://d.repec.org/n?u=RePEc:ecl:stabus:3483&r=gth 
By:  Srivastava, Vatsalya (Tilburg University, Center For Economic Research) 
Abstract:  This paper shows the existence of a sorry equilibrium in a game of imperfect public monitoring. In equilibrium, a selfimposed costly apology tendered after an accidental defection, makes private information public, allowing for continued cooperation. This cost cannot be too high or too low. Efficiency of the sorry equilibrium is evaluated and its welfare outcomes compared to other informal governance mechanisms and the formal legal system. With the possibility of accidental defections, it is shown that informal mechanisms have limitations, while formal legal systems can generate perverse incentives. The analysis demonstrates that apologies serve as a useful economic governance institution. 
Keywords:  apology; sorry; imperfect public monitoring; uncertainty; social norms; economics governance; Legal institutions; incentives; courts 
JEL:  D80 K40 D02 Z13 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:tiu:tiucen:252e94104c9f4a409ab7a8a501788803&r=gth 