
on Game Theory 
By:  Tatsuyoshi Saijo (School of Economics and Management, Kochi University of Technology); Takehito Masuda (Institute of Economic Research, Kyoto University); Yoshitaka Okano (School of Economics and Management, Kochi University of Technology); Takafumi Yamakawa 
Abstract:  After prisoner's dilemma, players can approve or reject the other's choice of cooperation or defection. If both players approve the other's choice, the outcome is the one they chose; however, if either rejects the other's choice, the outcome is the one they both defect. In theory, such approval mechanism implements cooperation in a backward elimination of weakly dominated strategies, although this is not the case in subgame perfect Nash equilibrium. By contrast, Varian's (1994) compensation mechanism implements cooperation in the latter but not in the former, which motivates the present study. The approval mechanism sessions yield a cooperation rate of 90% in the first period and 93.2% across periods, while the compensation mechanism sessions yield a rate of 63.3% in the first period and 75.2% across periods, indicating a significant difference. In addition, the backward elimination of weakly dominated strategies better predicts subjects' behavior than subgame perfect Nash equilibrium in both mechanism sessions. 
Keywords:  prisonerâ€™s dilemma, approval mechanism, cooperation, laboratory experiment, Seltenâ€™s index 
JEL:  C72 C73 C92 D74 P43 
Date:  2016–11 
URL:  http://d.repec.org/n?u=RePEc:kch:wpaper:sdes201615&r=gth 
By:  Dinko Dimitrov (Saarland University); Emiliya A. Lazarova (University of East Anglia); ShaoChin Sung (Aoyama Gakuin University) 
Abstract:  In many applications of coalition formation games, a key issue is that some desirable coalition structures are not elements of the core of these games. In these cases, it would be useful for an authority which aims to implement a certain outcome to know how far from the original game is the nearest game where the desirable outcome is part of the core. This question is at the center of this study. Focusing on hedonic games, we uncover previously unexplored links between such games and transferrable utility games, and develop a tailormade so lution concept for the transferrable utility game, the implementation core, to provide an answer to our question. 
Keywords:  hedonic game, implementation core, Kemeny distance, stability 
JEL:  C71 D71 
Date:  2016–09–29 
URL:  http://d.repec.org/n?u=RePEc:uea:ueaeco:2016_09&r=gth 
By:  Michel Grabisch (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics); Agnieszka Rusinowska (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics) 
Abstract:  We consider a model of opinion formation based on aggregation functions. Each player modifies his opinion by arbitrarily aggregating the current opinion of all players. A player is influential on another player if the opinion of the first one matters to the latter. A generalization of an influential player to a coalition whose opinion matters to a player is called an influential coalition. Influential players (coalitions) can be graphically represented by the graph (hypergraph) of influence, and convergence analysis is based on properties of the hypergraphs of influence. In the paper, we focus on the practical issues of applicability of the model w.r.t. a standard framework for opinion formation driven by Markov chain theory. For a qualitative analysis of convergence, knowing the aggregation functions of the players is not required, one only needs to know the set of influential coalitions for each player. We propose simple algorithms that permit us to fully determine the influential coalitions. We distinguish three cases: the symmetric decomposable model, the anonymous model, and the general model. JEL Classification: C7, D7, D85 
Keywords:  social network,opinion formation,aggregation function,influential coalition,algorithm 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:hal01387480&r=gth 
By:  SEMIN KIM (Yonsei University) 
Abstract:  We consider incentive compatible voting rules on the domain of singlepeaked preferences. In the environment where the value distributions are generic in the set of independent beliefs, we show that every incentive compatible rule satisfies the topsonly property. 
Keywords:  Incentive compatibility, Singlepeaked preferences, Topsonly property 
JEL:  C72 D01 D02 D72 D82 
Date:  2016–11 
URL:  http://d.repec.org/n?u=RePEc:yon:wpaper:2016rwp96&r=gth 
By:  Bos, Olivier; Ranger, Martin 
Abstract:  A two period labor market is considered in which workers’ quality is revealed in the second period. A signal – revealed to either workers, firms or both at the beginning of the first period – is correlated with the final quality. Under all assumptions about the distribution of information in the first period there exists an equilibrium in which firms only make offers in the second period and workers accept no offer in the first period. Nonetheless, early contracting is also an equilibrium if certain conditions on preferences of firms and workers are met. Workers have to be risk averse or firms risk loving with respect to expectations appropriate to the relevant information structure. Thus the conditions for unraveling depend on the information available to the two sides of the market. 
Keywords:  Unraveling, Risk Aversion, Asymmetric Information 
JEL:  C72 D82 D83 
Date:  2016–08–31 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:74785&r=gth 
By:  Simon Dato; Andreas Grunewald; Daniel Müller 
Abstract:  This paper provides a comprehensive analysis regarding strategic interaction under expectationbased lossaversion. First, we develop a coherent framework for the analysis by extending the equilibrium concepts of Koszegi and Rabin (2006, 2007) to strategic interaction and demonstrate how to derive equilibria. Second, we delineate how expectationbased lossaverse players differ in their strategic behavior from their counterparts with standard expectedutility preferences. Third, we analyze equilibrium play under expectationbased loss aversion and comment on the existence of equilibria. 
Keywords:  NonCooperative Games, ExpectationBased Loss Aversion, ReferenceDependent Preferences, Mixed Strategies 
JEL:  C72 D01 D03 D81 
Date:  2016–02 
URL:  http://d.repec.org/n?u=RePEc:bon:bonedp:bgse02_2016&r=gth 
By:  Anna Bogomolnaia (National Research University Higher School of Economics); Herve Moulin (National Research University Higher School of Economics); Fedor Sandomirskiy (National Research University Higher School of Economics); Elena Yanovskaya (National Research University Higher School of Economics) 
Abstract:  When utilities are additive, we uncovered in our previous paper (Bogomolnaia et al. "Dividing Goods or Bads under Additive Utilities") many similarities but also surprising differences in the behavior of the familiar Competitive rule (with equal incomes), when we divide (private) goods or bads. The rule picks in both cases the critical points of the product of utilities (or disutilities) on the efficiency frontier, but there is only one such point if we share goods, while there can be exponentially many in the case of bads. We extend this analysis to the fair division of mixed items: each item can be viewed by some participants as a good and by others as a bad, with corresponding positive or negative marginal utilities. We find that the division of mixed items boils down, normatively as well as computationally, to a variant of an all goods problem, or of an all bads problem: in particular the task of dividing the non disposable items must be either good news for everyone, or bad news for everyone. If at least one feasible utility profile is positive, the Competitive rule picks the unique maximum of the product of (positive) utilities. If no feasible utility profile is positive, this rule picks all critical points of the product of disutilities on the efficient frontier 
Keywords:  fair division of goods and bads, competitive equilibrium with equal incomes, Nash product, envyfreeness 
JEL:  D61 D63 D82 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:hig:wpaper:153/ec/2016&r=gth 
By:  SEMIN KIM (Yonsei University) 
Abstract:  We consider the performance and incentive compatibility of voting rules in a Bayesian environment: agents have independent private values, there are at least three alternatives, and monetary transfers are prohibited. First, we show that in a neutral environment, meaning alternatives are symmetric exante, essentially any expost Pareto efficient ordinal rule is incentive compatible. Importantly, however, we can improve upon ordinal rules. We show that we can design an incentive compatible cardinal rule which achieves higher utilitarian social welfare than any ordinal rule. Finally, we provide numerical findings about incentive compatible cardinal rules that maximize utilitarian social welfare. 
Keywords:  Ordinal rule, Pareto efficiency, Incentive compatibility, Bayesian mechanism design. 
JEL:  C72 D01 D02 D72 D82 
Date:  2016–11 
URL:  http://d.repec.org/n?u=RePEc:yon:wpaper:2016rwp94&r=gth 
By:  Roland Pongou (Department of Economics, University of Ottawa, Ottawa, ON); JeanBaptiste Tondji (Department of Economics, University of Ottawa, Ottawa, ON) 
Abstract:  We consider the problem of valuing inputs in a production environment in which input supply is uncertain. Inputs can be workers in a firm, risk factors for a disease, securities in a financial market, or nodes in a networked economy. Each input takes its values from a finite set, and uncertainty is modeled as a probability distribution over this set. First, we provide an axiomatic solution to our valuation problem, defining three intuitive axioms which we use to uniquely characterize a valuation scheme that we call the a priori Shapley value. Second, we solve the problem of valuing inputs a posteriori  that is, after observing output. This leads to the Bayesian Shapley value. Third, we consider the problem of rationalizing uncertainty when the inputs are rational workers supplying labor in a noncooperative production game in which payoffs are given by the Shapley wage function. We find that probability distributions over labor supply that can be supported as mixed strategy Nash equilibria always exist. We also provide an intuitive condition under which we prove the existence of a pure strategy Nash equilibrium. We present several applications of our theory to reallife situations. 
Keywords:  Input valuation, uncertainty, a priori Shapley value, Bayesian Shapley value, rationalizability 
JEL:  C70 D20 D80 J30 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:ott:wpaper:1617e&r=gth 
By:  Peter Backus (University of Manchester& Barcelona Institute of Economics (IEB)); María Cubel (Universitat de Barcelona); Matej Guid (University of Ljubljana); Santiago SánchezPages (Universitat de Barcelona); Enrique Lopez Manas (Google Developer Expert) 
Abstract:  There is a growing literature looking at how men and women respond differently to competition. We contribute to this literature by studying gender differences in performance in a highstakes and male dominated competitive environment, expert chess tournaments. Our findings show that women underperform compared to men of the same ability and that the gender composition of games drives this effect. Using within player variation in the conditionally random gender of their opponent, we find that women earn significantly worse outcomes against male opponents. We examine the mechanisms through which this effect operates by using a unique measure of within game quality of play. We find that the gender composition effect is driven by women playing worse against men, rather than by men playing better against women. The gender of the opponent does not affect a male player’s quality of play. We also find that men persist longer against women before resigning. These results suggest that the gender composition of competitions affects the behavior of both men and women in ways that are detrimental to the performance of women. Lastly, we study the effect of competitive pressure and find that players’ quality of play deteriorates when stakes increase, though we find no differential effect over the gender composition of games. 
Keywords:  Competition, Gender, Stereotype threat, Chess 
JEL:  D03 J16 J24 J70 L83 M50 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:ieb:wpaper:doc201627&r=gth 
By:  Bartke, Simon; Bosworth, Steven J.; Snower, Dennis; Chierchia, Gabriele 
Abstract:  This study analyzes the stability of preferences through the lens of psychological motives. We report the results of a public goods experiment in which subjects were induced with the motives of Care and Anger through autobiographical recall. Subjects' preferences, beliefs, and perceptions under each motive are compared with those of subjects experiencing a neutral autobiographical recall condition. We find that Care elicits significantly higher contributions than Anger, with Control treatment contributions in between. This is primarily driven by changes in conditional contribution schedules (measuring preferences) across treatments, though higher beliefs explain part of the effect that Care has on giving. These results are robust to checking for comprehension of the game's incentives. We also observe concomitant differences in attention to own and other's payoffs (using mouse tracking) as well as perceptions of the game's incentive structure (harmony)  particularly for subjects motivated by Anger. We interpret our findings as suggesting that people have access to multiple preferences that depend on how they perceive the decision context. 
Keywords:  public goods,motivation,stability of preferences,anger,care,framing 
JEL:  C92 H41 D64 D03 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:zbw:ifwkwp:2054&r=gth 
By:  Alexandre Skoda (Centre d'Economie de la Sorbonne) 
Abstract:  Let G = (N,E,w ) be a weighted communication graph (with weight function w on E ). For every subset A ? N, we delete in the subset E (A ) of edges with ends in A, all edges of minimum weight in E (A ). Then the connected components of the corresponding induced subgraph constitue a partition of A that we Pmin(A ). For every game (N , v ), we define the Pminrestricted game (N , v ) by v (A = ?F? Pmin (A) v(F ) for all A ? N. We prove that we can decide in polynomial time if there is inheritance of Fconvexity from N , v ) to the Pminrestricted game (N , v ) where Fconvexity is obtained by restricting convexity to connected subsets 
Keywords:  communication networks; cooperative game; convex game; restricted game; partitions; supermodularity; graph; complexity 
Date:  2016–07 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:16055&r=gth 
By:  Pierre Cardaliaguet (CEREMADE); CharlesAlbert Lehalle 
Abstract:  In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a Mean Field Game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader in front of a " background noise " (or " mean field "). In standard frameworks, the interactions between the large trader and the price are a temporary and a permanent market impact terms, the latter influencing the public price. In this paper the trader faces the uncertainty of fair price changes too but not only. He has to deal with price changes generated by other similar market participants, impacting the prices permanently too, and acting strategically. Our MFG formulation of this problem belongs to the class of " extended MFG ", we hence provide generic results to address these " MFG of controls ", before solving the one generated by the cost function of optimal trading. We provide a closed form formula of its solution, and address the case of " heterogenous preferences " (when each participant has a different risk aversion). Last but not least we give conditions under which participants do not need to instantaneously know the state of the whole system, but can " learn " it day after day, observing others' behaviors. 
Date:  2016–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1610.09904&r=gth 
By:  Philipp Moehlmeier (Bielefeld University); Agnieszka Rusinowska (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique, PSE  Paris School of Economics); Emily Tanimura (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  We develop a modification of the connections model by Jackson and Wolinsky (1996) that takes into account negative externalities arising from the connectivity of direct and indirect neighbors, thus combining aspects of the connections model and the coauthor model. We consider a general functional form for agents' utility that incorporates both the effects of distance and of neighbors' degree. Consequently, we introduce a framework that can be seen as a degreedistancebased connections model with both negative and positive externalities. Our analysis shows how the introduction of negative externalities modifies certain results about stability and efficiency compared to the original connections model. In particular, we see the emergence of new stable structures, such as a star with links between peripheral nodes. We also identify structures, for example, certain disconnected networks, that are efficient in our model but which could not be efficient in the original connections model. While our results are proved for the general utility function, some of them are illustrated by using a specific functional form of the degreedistancebased utility. 
Keywords:  network, externality, degree, distance, connections model 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:hal01387467&r=gth 
By:  Alejandro LeePenagos (School of Economics, University of Nottingham) 
Abstract:  Theoretical models have had difficulties to account, at the same time, for the most important stylized facts observed in experiments of the Voluntary Contribution Mechanism. A recent approach tackling that gap is Arifovic and Ledyard (2012), which implements social preferences in tandem with an evolutionary learning algorithm. However, the stylized facts have evolved. The model was not built to explain some of the most important findings in the public good games recent literature: that altruistic punishment can sustain cooperation. This paper extends their model in order to explain such recent findings. It focuses on fear of punishment, not punishment itself, as the key mechanism to sustain contributions to the public good. Results show that our model can replicate both qualitatively and quantitatively the main facts. Data generated by our model differs, on average, in less than 5% compared to relevant experiments with punishment in the lab. 
Keywords:  Public Good Games, Punishment, Agent Based Modelling, Learning Algorithms, Other Regarding Preferences, Bounded Rationality. 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201615&r=gth 
By:  Orestis Troumpounis; Dimitrios Xefteris; Bernard Grofman 
Abstract:  In twodimensional twoparty electoral competition under plurality rule, there are typically no equilibria, even when one of the dimensions refers to valence. The good news is that the introduction of either closed or open primaries acts as a stabilizing force since equilibria exist quite generally, serves as an arena for policy debates since all candidates propose differentiated platforms, and guarantees that each party's nominee is of higher quality than its primary opponent. Moreover, primaries tend to benefit the party whose median voter is closer to the overall median. The bad news is that the winner of the general election need not be the candidate with the highest overall quality since too competitive primaries can prove harmful. Given the differences between open and closed primaries, we show that the choice of primary type is particularly important and may determine the winner of the general election. 
Keywords:  Downsian model, primaries, valence 
JEL:  C62 C72 D72 
Date:  2016 
URL:  http://d.repec.org/n?u=RePEc:lan:wpaper:135286117&r=gth 