|
on Game Theory |
| By: | Giacomo Bonanno (Department of Economics, University of California Davis) |
| Abstract: | This is a draft of the first half of an open access textbook on game theory. I hope to complete the entire book by the end of 2015. After teaching game theory (at both the undergraduate and graduate level) at the University of California, Davis for 25 years, I decided to organize all my teaching material in a textbook. There are many excellent textbooks in game theory and there is hardly any need for a new one. However, there are two distinguishing features of this textbook: (1) it is open access and thus free, and (2) it contains an unusually large number of exercises (88 for the first half of the book) with complete and detailed answers. |
| Keywords: | Game theory, non-cooperative games, textbook |
| JEL: | C7 |
| Date: | 2015–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:cda:wpaper:15-2&r=gth |
| By: | Fabrizio Germano (Universitat Pompeu Fabra and Barcelona Graduate School of Economics); Peio Zuazo-Garin (Universitat Rovira i Virgili, Department d’Economia, CREIP and BRiDGE) |
| Abstract: | We study an interactive framework that explicitly allows for nonrational behavior. We do not place any restrictions on how players’ behavior deviates from rationality. Instead we assume that there exists a probability p such that all players play rationally with at least probability p, and all players believe, with at least probability p, that their opponents play rationally. This, together with the assumption of a common prior, leads to what we call the set of p-rational outcomes, which we define and characterize for arbitrary probability p. We then show that this set varies continuously in p and converges to the set of correlated equilibria as p approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The p-rational outcomes are easy to compute, also for games of incomplete information, and they can be applied to observed frequencies of play to derive a measure p that bounds from below the probability with which any given player chooses actions consistent with payoff maximization and common knowledge of payoff maximization. |
| Keywords: | strategic interaction, correlated equilibrium, robustness to bounded rationality, approximate knowledge, incomplete information, measure of rationality, experiments |
| JEL: | C72 D82 D83 |
| Date: | 2015–11–02 |
| URL: | http://d.repec.org/n?u=RePEc:aim:wpaimx:1551&r=gth |
| By: | Dutta, Bhaskar (Department of Economics University of Warwick); Vohra, Rajiv (Brown University) |
| Abstract: | In the study of farsighted coalitional behavior, a central role is played by the von Neumann-Morgenstern (1944) stable set and its modification that incorporates farsightedness. Such a modification was first proposed by Harsanyi (1974) and has recently been re-formulated by Ray and Vohra (2015). The farsighted stable set is based on a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional ‘moves’ in which each coalition that is involved in the sequence eventually stands to gain. However, it does not require that each coalition make a maximal move, i.e., one that is not Pareto dominated (for the members of the coalition in question) by another. Nor does it restrict coalitions to hold common expectations regarding the continuation path from every state. Consequently, when there are multiple continuation paths the farsighted stable set can yield unreasonable predictions. We resolve this difficulty by requiring all coalitions to have common rational expectations about the transition from one outcome to another. This leads to two related concepts: the rational expectations farsighted stable set (REFS) and the strong rational expectations farsighted stable set (SREFS). We apply these concepts to simple games and to pillage games to illustrate the consequences of imposing rational expectations for farsighted stability. |
| Keywords: | stable sets ; farsightedness ; consistency ; maximality ; rational expectations ; simple games ; pillage games. Classification -JEL: C71 ; D72 ; D74 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:1090&r=gth |
| By: | Eric Bahel (Department of Economics, Virginia Polytechnic Institute and State University); Christian Trudeau (Department of Economics, University of Windsor) |
| Abstract: | The paper examines minimal cost arborescence problems, which generalize the well-known minimal cost spanning tree (mcst) problems. We propose a new family of cost sharing methods that are easy to compute, as they closely relate to the network-building algorithm. These methods, called minimal incoming cost rules for arborescences (MICRAs), include as a particular case the extension of the folk solution introduced by Dutta and Mishra (2012). A simpler computational procedure thus obtains for this method. We also provide new axiomatizations of (a) the set of stable and symmetric MICRAs and (b) the folk solution. Finally, we closely examine two remarkable MICRAs. The first one relates to the cycle-complete rule for mcst problems introduced in Trudeau (2012). The second one contrasts with the folk rule by fully rewarding agents who help others connect to the source. |
| Keywords: | arborescence problems; stable allocations, minimal incoming cost rules, leftover cost matrix |
| JEL: | C71 D63 |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:wis:wpaper:1601&r=gth |
| By: | Markus Kinateder (Departamento de Economía, Edificio de Amigos, Universidad de Navarra); Hubert Janos Kiss (Momentum Game Theory Research Group - Institute of Economics - Centre for Economic and Regional Studies - Hungarian Academy of Sciences and Department of Economics, Eötvös Loránd University); Agnes Pinter (Department of Economic Analysis, Universidad Autónoma de Madrid) |
| Abstract: | There is an asymmetry regarding what previous decisions depositors may observe when choosing whether to withdraw or keep the money deposited: it is more likely that withdrawals are observed. We study how decision-making changes if depositors are able to make their decision to keep their funds in the bank visible to subsequent depositors at a cost. We show theoretically in a Diamond-Dybvig setup that without this signaling option multiple equilibria are possible, while signaling makes the no-run outcome the unique equilibrium. We test if the theoretical predicitions hold in a lab experiment. We find that indeed when signaling is available, bank runs are less likely to arise and signaling is extensively used. |
| Keywords: | Bank runs, Asymmetric information, Experimental evidence, Signaling |
| JEL: | C72 C91 D80 G21 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1553&r=gth |
| By: | Maurya, Amit Kumar |
| Abstract: | We study a model of multilateral bargaining in which a buyer attempts to assemble objects owned by multiple sellers. Players can (non-cooperatively) opt out of the bargaining whenever they want. The presence of this option results in an equilibrium in which the buyer implements the project immediately and grabs the entire surplus. It also mitigates the inefficiency associated with nontransparent bargaining protocol. These results are in stark contrast to those obtained in Roy Chowdhury and Sengupta (2012). |
| Keywords: | Multilateral bargaining, Opt Out, Outside options, Efficiency, Non-transparency |
| JEL: | C72 C78 D23 |
| Date: | 2015–12–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:68681&r=gth |
| By: | Tobias Regner (School of Economics and Business Administration, Friedrich-Schiller-University Jena); Astrid Matthey (Max Planck Institute of Economics, Jena) |
| Abstract: | By now there is substantial experimental evidence that people make use of 'moral wiggle room' (Dana et al., 2007), that is, they tend to exploit moral excuses for selfish behavior. However, this evidence is limited to dictator games. In our experiment, a trust game variant, we study whether moral wiggle room also prevails, when reciprocity is a potential motivation for being generous. Trustees' back transfer choices are elicited for five different transfer levels of the trustor. Moreover, we ask trustees to provide their back transfer schedule for different scenarios that vary the implementation probability of the back transfer. This design allows us to identify subjects who reciprocate and analyze how these reciprocators respond to the provision of moral wiggle room. Our results suggest that moral wiggle room exists as well in the context of reciprocity. Among our subjects, 40% of the reciprocators exploited moral wiggle room. |
| Keywords: | social preferences, pro-social behavior, experiments, reciprocity, moral wiggle room, self-image concerns |
| JEL: | C72 C91 D03 D80 |
| Date: | 2015–12–22 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2015-027&r=gth |
| By: | Hart, Sergiu (Department of Economics, Institute of Mathematics, and Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem.); Kremer, Ilan (Department of Economics, Business School, and Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem; Department of Economics, University of Warwick); Perry, Motty (Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem; Department of Economics, University of Warwick.) |
| Abstract: | An evidence game is a strategic disclosure game in which an informed agent who has some pieces of verifiable evidence decides which ones to disclose to an uninformed principal who chooses a reward. The agent, regardless of his information, prefers the reward to be as high as possible. We compare the setup where the principal chooses the reward after the evidence is disclosed to the mechanism-design setup where he can commit in advance to a reward policy. The main result is that under natural conditions on the truth structure of the evidence, the two setups yield the same equilibrium outcome. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:1091&r=gth |
| By: | Balazs Sziklai (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences); Erel Segal-Halevi (Bar-Ilan University Israel) |
| Abstract: | We study the monotonicity properties of solutions in the classic problem of fair cake-cutting – dividing a single heterogeneous resource among agents with subjective utilities. Resource- and population-monotonicity relate to scenarios where the cake, or the number of participants who divide the cake, changes. It is required that the utility of all participants change in the same direction: either all of them are better-off (if there is more to share) or all are worse-off (if there is less to share). We formally introduce these concepts to the cake-cutting setting and present a meticulous axiomatic analysis. We show that classical cake-cutting protocols, like the Cut and Choose, Banach-Knaster, Dubins–Spanier and many other fail to be monotonic. We also show that, when the allotted pieces must be contiguous, proportionality and Pareto-optimality are incompatible with each of the monotonicity axioms. We provide a resource-monotonic protocol for two players and show the existence of rules that satisfy various combinations of contiguousness, proportionality, Pareto-optimality and the two monotonicity axioms. |
| Keywords: | resource-monotonicity, population-monotonicity, cake-cutting, leximin divisions, equitable divisions |
| JEL: | D63 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1552&r=gth |
| By: | Balazs Sziklai (Momentum Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences) |
| Abstract: | The group identification literature mostly revolves around the problem of identifying individuals in the community who belong to groups with ethnic or religious identity. Here we use the same model framework to identify individuals who play key role in some sense. In particular we will focus on expert selection in social networks. Ethnic groups and experts groups need completely different approaches and different type of selection rules are successful for one and for the other. We drop monotonicity and independence, two common requirements, in order to achieve stability, a property which is indispensable in case of expert selection. The idea is that experts are more effective in identifying each other, thus the selected individuals should support each others membership. We propose an algorithm based on the so called top candidate relation. We establish an axiomatization to show that it is theoretically well-founded. Furthermore we present a case study using citation data to demonstrate its effectiveness. We compare its performance with classical centrality measures. |
| Keywords: | Group identification, Expert selection, Stability, Citation analysis, Nucleolus |
| JEL: | D71 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1549&r=gth |
| By: | Proto, Eugenio (Department of Economics, University of Warwick); Rustichini, Aldo (Department of Economics, University of Minnesota); Sofianos, Andis (Department of Economics, University of Warwick) |
| Abstract: | Intelligence affects the social outcomes of groups. A systematic study of the link is provided in an experiment where two groups of subjects with different levels of intelligence, but otherwise similar, play a repeated prisoner's dilemma. Initial cooperation rates are similar, but increase in the groups with higher intelligence to reach almost full cooperation, while they decline in the groups with lower intelligence. Cooperation of higher intelligence subjects is payo sensitive and not automatic: in a treatment with lower continuation probability there is no difference between different intelligence groups. |
| Keywords: | Repeated Prisoner's Dilemma ; Cooperation ; Intelligence |
| JEL: | C73 C91 C92 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:1101&r=gth |
| By: | Thomas Eichner; Rüdiger Pethig |
| Keywords: | climate coalition, deposit, fuel, Nash, self-enforcing IEA |
| JEL: | C72 Q38 Q58 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:sie:siegen:176-15&r=gth |
| By: | Rafael Hortala-Vallve (London School of Economics); Aniol Llorente-Saguer (Queen Mary University of London) |
| Abstract: | We study a version of the Colonel Blotto game where valuations across battlefields are heterogeneous and asymmetric. These games can exhibit unique pure strategy equilibria, some of which are non-monotonic with respect to the battlefield valuations. We test our theoretical predictions in the laboratory and find low initial levels of equilibrium play but substantial learning throughout the experiment. Learning is higher for games with monotonic equilibria. Finally, we find that deviations from equilibrium predictions benefit aggregate welfare. |
| Keywords: | Colonel Blotto, Non-zero sum, Experiments |
| JEL: | C92 D70 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp779&r=gth |
| By: | Arianna Galliera (Department of Economics, University Of Venice Cà Foscari); Noemi Pace (Department of Economics, University Of Milan, Bicocca) |
| Abstract: | The incentive scheme selected in a laboratory experiment might trigger different type of behavior in participants. This paper is an attempt to screen the strategies adopted by agents in a bargaining game when buyer and seller have partly conflicting interests and are asymmetrically informed. We allow participants to choose the incentive scheme through which they will be paid at the end of the experiment controlling for past experience and individual characteristics. It is well known that payment method is highly correlated to the risk preferences shown by individuals, but little research is devoted to the analysis of the behavior induced by Random Lottery Incentive scheme (RLI for short) and Cumulative Scheme payment (CS for short) both on individual and social results. This paper aims to fill the gap. |
| Keywords: | bargaining, experiment, gender, payment scheme. |
| JEL: | C78 C91 D82 J16 J33 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2015:33&r=gth |
| By: | Laurent Bouton (Georgetown University, Université Libre de Bruxelles, CEPR and NBER); Micael Castanheira (Université Libre de Bruxelles, FNRS and CEPR); Aniol Llorente-Saguer (Queen Mary University of London) |
| Abstract: | We propose a theory-based experimental approach to compare the properties of <i>approval voting</i> (AV) with those of <i>plurality</i>. This comparison is motivated by the theoretical predictions that, in our aggregate uncertainty setup, AV should produce close to first-best outcomes, while plurality will not. The experiment shows, first, that welfare gains are substantial. Second, both aggregate and individual responses are in line with theoretical predictions, and thus with strategic voting. Finally, subjects' behavior under AV highlights the need to study equilibria in asymmetric strategies. |
| Keywords: | Multicandidate elections, Information aggregation, Plurality, Approval Voting, Laboratory experiments |
| JEL: | C72 C92 D70 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp777&r=gth |
| By: | Yannis Katsoulacos (Athens University of Economics and Business, Athens, Greece); Evgenia Motchenkova (VU University Amsterdam, the Netherlands); David Ulph (University of St Andrews, St Andrews, Fife, Great Britain) |
| Abstract: | This paper develops a model of the birth and death of cartels in the presence of enforcement activities by a Competition Authority (CA). We distinguish three sets of interventions: (a) detecting, prosecuting and penalizing cartels; (b) actions that aim to stop cartel activity in the short-term, immediately following successful prosecution; (c) actions that aim to prevent the re-emergence of prosecuted cartels in the longer term. The last two intervention activities have not been analyzed in the existing literature. In addition we take account of the structure and toughness of penalties. In this framework the enforcement activity of a CA causes industries in which cartels form to oscillate between periods of competitive pricing and periods of cartel pricing. We determine the impact of CA activity on deterred, impeded, and suffered harm. We derive measures of both the total and the marginal effects on welfare resulting from competition authority interventions and show how these break down into measures of the Direct Effect of interventions (i.e. the effect due to cartel activity being impeded) and two Indirect/Behavioral Effects – on Deterrence and Pricing. Finally, we calibrate the model and estimate the fraction of the harm that CAs remove as well as the magnitude of total and marginal welfare effects of anti-cartel interventions. |
| Keywords: | Antitrust Enforcement; Antitrust Law; Cartel; Oligopoly; Repeated Games |
| JEL: | L4 K21 D43 C73 |
| Date: | 2016–01–07 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150141&r=gth |
| By: | John Kennes (Department of Economics and Business Economics, Aarhus University, Denmark); Daniel le Maire (Department of Economics, University of Copenhagen, Denmark) |
| Abstract: | We generalize McAfee’s (1993) game of competing sellers to the case of heterogeneous sellers. In the generalized McAfee (GM) game, the equilibrium expected job offer distribution of each worker (seller) type evolves over time as a function of stochastic events. We derive a tractable method of solving the GM game. We estimate, using non-parametric methods, a close fit between a benchmark GM game and a cross-section of Danish data on productivity and unemployment. The theoretical properties of the GM game, which relate to on-the-job search, assortative matching, aggregate and match specific shocks, and the equivalence of alternative games, are also characterized. |
| Keywords: | Auctions, assortative matching, wage dispersion, aggregate shocks, on-the-job search |
| JEL: | J64 J63 E32 |
| Date: | 2016–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:aah:aarhec:2016-02&r=gth |