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on Game Theory |
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Issue of 2009‒09‒26
twenty-two papers chosen by Laszlo A. Koczy Budapest Tech and Maastricht University |
| By: | Francesco Ciardiello; Crescenzio Gallo |
| Abstract: | We propose an algorithm for computing "main stable sets" recently introduced by Ciardiello, Di Liddo (2009) on effectiveness form coalitional games modeled through a directed pseudograph. The algorithm is based upon a graph traversing method exploring extended paths minimal in coalitions and we study some its interesting computational aspects for making these stability concepts as useful tools for decision theory. |
| Keywords: | Algorithmic game theory; coalitional games; dominance relations; stable sets; graph theory. |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:ufg:qdsems:08-2009&r=gth |
| By: | Francesco Ciardiello |
| Abstract: | I present a proof on finiteness of Von Neumann and Morgenstern's majority stable sets in multidimensional voting games in the case of differentiable utility functions on Rk and 3 players. The central hypothesis is based on a light separation property which is real common for family of functions on R^k. Under the same hypotheses, the majority core is empty except for degenerate cases. |
| Keywords: | Stable sets; Voting game; Convexity. |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:ufg:qdsems:16-2009&r=gth |
| By: | William Thomson (University of Rochester) |
| Abstract: | This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162). |
| Keywords: | Nash's bargaining model, Nash solution, Kalai-Smorodinsky solution, Egalitarian solution |
| JEL: | D63 D70 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:554&r=gth |
| By: | Marta Biancardi; Francesco Ciardiello |
| Abstract: | In this paper we propose the state of art in the theory of coalitional games in effectiveness form without bargaining between coalitions. We study some solution concepts: The largest consistent set (Chwe, 1994); the largest cautious consistent set (Mauleon et al., 2004); the credible consistent set (Bhattacharya, 2002); standard stable behaviors (Xue, 1998). A series of examples, showing main features and differences between these solutions, are presented in order to outline some drawbacks and positive aspects in the philosophical framework of stability concepts. |
| Keywords: | coalitonal games; stable sets; farsightedness. |
| JEL: | C62 C71 |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:ufg:qdsems:11-2009&r=gth |
| By: | László Á. Kóczy (Keleti Faculty of Economics, Budapest Tech and Department of Economics, Maastricht University) |
| Abstract: | We study coalitional games where the proceeds from cooperation depend on the entire coalition structure. The coalition structure core (Kóczy, GEB, 2007) is a generalisation of the coalition structure core for such games. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core. In order to extend past results to games that are not totally balanced (understood in this special setting) we introduce subgame-consistency that requires perfectness in relevant subgames only, while subgames that are never reached are ignored. |
| Keywords: | partition function, externalities, implementation, recursive core, stationary perfect equilibrium, time consistent equi- librium |
| JEL: | C71 C72 |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:pkk:wpaper:0905&r=gth |
| By: | Attila Tasnádi |
| Abstract: | We consider a possible game-theoretic foundation of Forchheimer’s model of dominant-firm price leadership based on quantity-setting games with one large firm and many small firms. If the large firm is the exogenously given first mover, we obtain Forchheimer’s model. We also investigate whether the large firm can emerge as a first mover of a timing game. Keywords |
| Keywords: | Forchheimer; Dominant firm; Price leadership. |
| JEL: | D43 L13 |
| Date: | 2009–09–25 |
| URL: | http://d.repec.org/n?u=RePEc:eei:rpaper:eeri_rp_2009_25&r=gth |
| By: | Francesco Ciardiello; Anindya Bhattacharya; Victoria Brosi |
| Abstract: | In this work we explore some properties of on-Neumann-Morgenstern stable sets in the environment of multidimensional spatial voting situations. In our framework, the set of outcomes under consideration is some compact and convex subset of some finite dimensional Euclidean space and any majority coalition can enforce any outcome from another. Among the more significant results, we show that contrary to the well-known claim in Cox, 1987 (repeated in many subsequent works), a stable set in such an environment does not necessarily coincide with the core even when the core is non-empty. We also study when such a stable set may be finite. |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:ufg:qdsems:05-2009&r=gth |
| By: | Roman M. Sheremeta; Jingjing Zhang |
| Abstract: | This experimental study explores how communication influences efficiency, trust and trustworthiness in a small group when one member is left out of communication. To study this problem, we introduce a novel three-player trust game where player 1 can send any portion of his endowment to player 2. The amount sent gets tripled. Player 2 decides how much to send to player 3. The amount is again tripled, and player 3 then decides the allocation among the three players. The baseline treatment with no communication shows that on average players 1 and 2 send significant amounts and player 3 reciprocates even though all players are randomly regrouped every period. When we add communication between players 2 and 3, the amounts sent and returned between these two increase. The interesting finding is that there are external effects of communication: player 1 who is outside communication sends 60% more and receives 140% more than in the no communication treatment. As a result, social welfare and efficiency increase from 48% to 73%. |
| Keywords: | Multi-level Trust Games; Experiments; Reciprocity; Communication |
| JEL: | C72 C91 D72 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:mcm:deptwp:2009-07&r=gth |
| By: | Béal, Sylvain; Rémila, Eric; Solal, Philippe |
| Abstract: | We present the axiom of weighted component fairness for the class of forest games, a generalization of component fairness introduced by Herings, Talman and van der Laan (2008) in order to characterize the average tree solution. Given a system of weights, component eciency and weighted component fairness yield a unique allocation rule. We provide an analysis of the set of allocation rules generated by component eciency and weighted component fairness. This allows us to provide a new characterization of the random tree solutions. |
| Keywords: | (Weighted) component fairness ; Core ; Graph games ; Alexia value ; Harsanyi solutions ; Random tree solutions. |
| JEL: | C71 |
| Date: | 2009–08–18 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:17455&r=gth |
| By: | Mihm, Maximilian (Cornell University); Toth, Russell (Cornell University); Lang, Corey (Cornell University) |
| Abstract: | We consider strategic interaction on a network of heterogeneous long-term relationships. The bilateral relationships are independent of each other in terms of actions and realized payoffs, and we assume that information regarding outcomes is private to the two parties involved. In spite of this, the network can induce strategic interdependencies between relationships, which facilitate efficient outcomes. We derive necessary and sufficient conditions that characterize efficient equilibria of the network game in terms of the architecture of the underlying network, and interpret these structural conditions in light of empirical regularities observed in many social and economic networks. |
| JEL: | C73 D82 D85 |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:corcae:09-07&r=gth |
| By: | Aguirregabiria, Victor |
| Abstract: | This document describes program code for the solution and estimation of dynamic discrete games of incomplete information using the Nested Pseudo Likelihood (NPL) method in Aguirregabiria and Mira (2007). The code is illustrated using a dynamic game of store location by retail chains, and actual data from McDonalds and Burger King. |
| Keywords: | Estimation of Dynamic Games; Nested Pseudo Likelihood Algorithm; Program Code |
| JEL: | C13 C63 C87 C25 C73 |
| Date: | 2009–09–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:17329&r=gth |
| By: | Elisabeth Gugl; Justin Leroux |
| Abstract: | Consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions precludes transferable utility (a property we call “Almost TU”). We show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash Bargaining and the utilitarian solutions are special cases). We apply the result to household decisionmaking in the contex of the Rotten Kid Theorem and in evaluating a change in family taxation. |
| Keywords: | Axiomatic Bargaining, Solidarity, Transferable Utility, FamilyT-taxation, Rotten Kid Theorem |
| JEL: | C71 D63 D13 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:lvl:lacicr:0938&r=gth |
| By: | Sophia Chong; Pablo Guillen |
| Abstract: | This paper compares individual with collective contracts using modified repeated gift exchange games. The game had two variations, both following a partner design. In the individual variation different workers in the same firm can receive separate wages, and in the collective variation all workers in the same firm receive the same wage. These two variations are played altering the order. Thus the experiment has four treatments, two within subjects (regarding the games played) and two between subjects (regarding the order in which the games are played). We did not find significant differences between the two variations of the game when subjects had no experience. However, individual agreements turned out to be more efficient when subjects have previously experienced collective agreements. This result suggests subjects learned to reciprocate when they played the collective variation followed by the individual variation of the gift exchange game. |
| Keywords: | laboratory experiments, gift exchange, collective contracts. |
| JEL: | C92 |
| Date: | 2009–09–14 |
| URL: | http://d.repec.org/n?u=RePEc:gra:wpaper:09/05&r=gth |
| By: | Nejat Anbarci; Ching-jen Sun |
| Abstract: | Most real-life bargaining is resolved gradually; two parties reach intermediate agreements without knowing the whole range of possibilities. These intermediate agreements serve as disagreement points in subsequent rounds. Cooperative bargaining solutions ignore these dynamics and can therefore yield accurate predictions only if they are robust to its specification. We identify robustness criteria which are satisfied by four of the best-known bargaining solutions, the Nash, Kalai-Smorodinsky, Proportional and Discrete Raiffa solutions. We show that the “robustness of intermediate agreements” plus additional well-known and plausible axioms, provide the first characterization of the Discrete Raiffa solution and novel axiomatizations of the other three solutions. Hence, we provide a unified framework for comparing these solutions’ bargaining theories. |
| Keywords: | Nash’s bargaining problem, robustness, intermediate agreements, the Discrete Raiffa solution, the Nash solution, the Kalai-Smorodinsky solution, Proportional solutions. |
| JEL: | C78 D74 |
| Date: | 2009–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:dkn:econwp:eco_2009_14&r=gth |
| By: | Matthias Hanauske; Jennifer Kunz; Steffen Bernius; Wolfgang K\"onig |
| Abstract: | The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as the consequences of the financial crisis exhibit, it would be desirable to change the 'rules of the game' in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the in literature well-known Hawk-Dove game by a quantum approach, we can show that dependent on entanglement, also evolutionary stable strategies can emerge, which are not predicted by classical evolutionary game theory and where the total economic population uses a non aggressive quantum strategy. |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0904.2113&r=gth |
| By: | Timothy N. Cason; Roman M. Sheremeta; Jingjing Zhang |
| Abstract: | Costless pre-play communication has been found to effectively facilitate coordination and enhance efficiency by increasing individual payoffs in games with Pareto-ranked equilibria. We report an experiment in which two groups compete in a weakest-link contest by expending costly efforts. Allowing group members to communicate before choosing efforts leads to more aggressive competition and greater coordination, but also results in substantially lower payoffs than a control treatment without communication. Our experiment thus provides evidence that communication can reduce efficiency in competitive coordination games. This contrasts sharply with experimental findings from public goods and other coordination games, where communication enhances efficiency and often leads to socially optimal outcomes. |
| Keywords: | Contest; Between-group Competition; Within-group Competition; Cooperation; Coordination; Free-riding; Experiments |
| JEL: | C71 C72 C91 C92 D72 H41 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:mcm:deptwp:2009-09&r=gth |
| By: | Karol Wawrzyniak; Wojciech Wislicki |
| Abstract: | We present a comprehensive study of utility function of the minority game in its efficient regime. We develop an effective description of state of the game. For the payoff function $g(x)=\sgn (x)$ we explicitly represent the game as the Markov process and prove the finitness of number of states. We also demonstrate boundedness of the utility function. Using these facts we can explain all interesting observable features of the aggregated demand: appearance of strong fluctuations, their periodicity and existence of prefered levels. For another payoff, $g(x)=x$, the number of states is still finite and utility remains bounded but the number of states cannot be reduced and probabilities of states are not calculated. However, using properties of the utility and analysing the game in terms of de Bruijn graphs, we can also explain distinct peaks of demand and their frequencies. |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:0907.3231&r=gth |
| By: | Marta Biancardi; Giovanni Villani |
| Abstract: | The paper investigates the stability of the International Environmental Agreement in a model of emission reduction. We consider a two stage game, in which in the first stage each country decides whether or not to join the agreement while, in the second stage, the quantity of emissions reduction is chosen. Agents may act cooperatively, building coalitions and acting according to the interest of the coalition, or they make their choices taking care of their individual interest only. Unlike conventional coalition stability models, we assume that countries are not identical but they are divided in two different kinds: developing countries and developed ones; the first have a lower attention about environmental pollution than developed ones. According to environmental awareness, stable coalitions of different sizes occur. On this subject, we present a Maple algorithm to compute the optimal costs and the abatement level for each coalition forms assuming an arbitrary number of developed and developing countries and to determine the internal and the external stability. In order to expand a coalition of any size to the grand coalition, which reaches the greatest abatement level and the lowest aggregate costs, we introduce monetary transfers. |
| Keywords: | IEA; Coalition stability; Implementation; Monetary Transfers |
| JEL: | F50 C70 C60 H23 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:ufg:qdsems:09-2009&r=gth |
| By: | Masahiro Okuno-Fujiwara (Faculty of Economics, University of Tokyo); Hirokazu Takizawa (Faculty of Economics, Chuo University); Noriyuki Yanagawa (Faculty of Economics, University of Tokyo); Yasunori Watanabe (School of Grobal Studies, Tama University) |
| Abstract: | This paper analyzes a model of coordination where two agents attempt to coordinate their actions through communication. One agent (Sender) is engaged in finding the true state of nature in a stochastic environment and the action that best fits the state. The other agent (Receiver) in turn tries to ``understand'' the Sender's message and chooses his own action. Since the communication succeeds only probilistically, so does the coordination. In our model, two different modes of coordination are identified: the integral-type coordination based on the communication of soft information and the default-type coordination based on the predetermined default value. We find that the agents might choose the latter mode of coordination when the cost arising from the failed communication is high relative to the benefit from coordinating on the state-contingent best actions. Applications to the economics of organization are also discussed. |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:tky:jseres:2009cj213&r=gth |
| By: | Edward Cartwright; Joris Gillet; Mark Van Vugt |
| Abstract: | We analyze a coordination game characterised by varying degrees of conflict of interest, incentive to coordinate and information asymmetry. The primary objective is to question whether endogenous leadership better enables coordination. A secondary objective is to question whether preference and information asymmetries cue who should lead. Both experimental and theoretical results are provided. We find that in theory leadership should allow coordination, whether or not preferences are common knowledge. In practice we found that leadership did enable coordination but information about others preferences also helped. This was explained as due to some participants being too eager to lead. Which may be surprising given that we find, both in theory and in practice, leaders get relatively low payoffs, particularly when preferences are private information. |
| Keywords: | Coordination game; Conflict of interest; leadership |
| JEL: | C72 D11 D80 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:ukc:ukcedp:0913&r=gth |
| By: | Mongin, Philippe |
| Abstract: | The paper has a twofold aim. On the one hand, it provides what appears to be the first game-theoretic modeling of Napoleon’s last campaign, which ended dramatically on 18 June 1815 at Waterloo. It is specifically concerned with the decision Napoleon made on 17 June 1815 to detach part of his army against the Prussians he had defeated, though not destroyed, on 16 June at Ligny. Military historians agree that this decision was crucial but disagree about whether it was rational. Hypothesizing a zero-sum game between Napoleon and Blücher, and computing its solution, we show that it could have been a cautious strategy on the former's part to divide his army, a conclusion which runs counter to the charges of misjudgement commonly heard since Clausewitz. On the other hand, the paper addresses methodological issues. We defend its case study against the objections of irrelevance that have been raised elsewhere against “analytic narratives”, and conclude that military campaigns provide an opportunity for successful application of the formal theories of rational choice. Generalizing the argument, we finally investigate the conflict between narrative accounts – the historians' standard mode of expression – and mathematical modeling. |
| Keywords: | Napoléon; Blücher; Grouchy; Waterloo; military history; rational choice theories; game theory; zero-sum two-person games; analytical narrative |
| JEL: | B49 C72 N43 |
| Date: | 2009–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:heccah:0915&r=gth |
| By: | Roman M. Sheremeta; Jingjing Zhang |
| Abstract: | This paper reports an experiment that examines whether groups can make better decisions than individuals in contests. Our experiment replicates previous findings that individual players significantly overbid relative to theoretical predictions, incurring substantial losses. There is high variance in individual bids and strong heterogeneity across individual players. The new findings of our experiment are that groups make bids that are 25% lower, bids have less variance, and there is less heterogeneity across groups than across individuals. Therefore, groups receive significantly higher and more homogeneous payoffs than individuals. We elicit individual and group preferences towards risk using simple lotteries. The results indicate that groups make less risky decisions, which is a possible explanation for lower bids in contests. Most importantly, we find that groups learn to make lower bids from communication and negotiation between group members. |
| Keywords: | Rent-seeking; Contest; Experiments; Risk; Over-dissipation; Group Decision-making |
| JEL: | C72 C91 C92 D72 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:mcm:deptwp:2009-05&r=gth |