nep-gth New Economics Papers
on Game Theory
Issue of 2013‒06‒09
ten papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. Accepting Zero in the Ultimatum Game: Selfish Nash Response? By Gianandrea Staffiero; Filippos Exadaktylos; Antonio M. Espín
  2. A Stochastic Search Algorithm for the Computation of Perfect and Proper Equilibria By Stuart McDonald; Liam Wagner
  3. Endogenous vs. Exogenous Transmission of Information: An Experiment By Aurora García-Gallego; Penélope Hernández-Rojas; Amalia Rodrigo-González
  4. Incomplete Information Models of Guilt Aversion in the Trust Game By Giuseppe Attanasi; Pierpaolo Battigalli; Elena Manzoni
  5. Stochastic games with short-stage duration By Abraham Neyman
  6. Indirect Reciprocity, Golden Opportunities for Defection, and Inclusive Reputation By Hannes Rusch; Max Albert
  7. Complements and Substitutes in Generalized Multisided Assignment Economies By Oriol Tejada
  8. Unilateral emission reductions can lead to Pareto improvements when adaptation to damages is possible By Klaus Eisenack; Leonhard Kähler
  9. Gender Differences in Cooperation: Experimental Evidence on High School Students By Molina, José Alberto; Gimenez-Nadal, Jose Ignacio; Cuesta, José A.; Garcia-Lazaro, Carlos; Moreno, Yamir; Sanchez, Angel
  10. A degree-distance-based connections model with negative and positive externalities By Philipp Möhlmeier; Agnieszka Rusinowska; Emily Tanimura

  1. By: Gianandrea Staffiero (Universitat Pompeu Fabra); Filippos Exadaktylos (BELIS, Murat Sertel Center for Advanced Economic Studies,Istanbul Bilgi University); Antonio M. Espín
    Abstract: The rejection of unfair proposals in ultimatum games is often quoted as evidence of other-regarding preferences. In this paper we focus on those responders who accept any proposals, setting the minimum acceptable offer (MAO) at zero. While this behavior could result from the randomization between the two payoff-maximizing strategies (i.e. setting MAO at zero or at the smallest positive amount), it also implies that the opponent’s payoff is maximized and the “pie†remains intact. We match subjects’ behavior as ultimatum responders with their choices in the dictator game, in two large-scale experiments. We find that those who set MAO at zero are the most generous dictators. Moreover, they differ substantially from responders whose MAO is the smallest positive offer, who are the greediest dictators. Thus, an interpretation of zero MAOs in terms of selfish, payoff-maximizing behavior could be misleading. Our evidence indicates that the restraint from punishing others can be driven by altruism and by the desire to maximize social welfare.
    Keywords: ultimatum game, dictator game, altruism, social welfare, costly punishment, selfishness, social preferences
    JEL: C93 C91 D03 C70
    Date: 2012–01
  2. By: Stuart McDonald (School of Economics, The University of Queensland); Liam Wagner (School of Economics, University of Queensland)
    Abstract: This paper shows that stochastic search algorithms can be used to compute the perfect and proper equilibria of finite games. These type of equilibria use perturbations as a means of escape from local equilibria. Intuitively, there is always a small probability that an agent will select alternative strategy, even if that strategy is sub-optimal. This allows agents to escape from local equilibria in much the same way that stochastic search algorithms (like genetic algorithms and simulated annealing, for example) escape from local equilibria. This paper constructs a possibility result showing that if this equilibrium exists, then it can be found by using a stochastic search algorithm. This paper also shows by example, using the three player extensive game "Selten's Horse", that stochastic search can be used to locate a perfect equilibrium in an extensive form game.
    Keywords: Perfect and proper equilibria; computational methods; stochastic search.
    JEL: C72 C73 C62 G
    Date: 2013–05–25
  3. By: Aurora García-Gallego (LEE & Department of Economics, Universitat Jaume I, Castellón, Spain); Penélope Hernández-Rojas (ERI-CES & Department of Economic Analysis, University of Valencia, Spain); Amalia Rodrigo-González (Department of Business Finance, University of Valencia, Spain)
    Abstract: Based on Gossner, Hernández and Neyman’s (2006) 3-player game (hereafter GHN) we analyze communication efficiency in the lab. In that game, player 1 represents random nature an i.i.d. procedure, player 2 is a fully informed player (wiser), and player 3 is the less informed player (agent). The game is repeated and players 2 and 3 get 1 if both actions match nature’s actions and 0 otherwise. We propose an experiment following this game. We implement two treatments: one without chat (NC) and one with chat (C). In the treatment with chat, players may first send messages to each other through an online chat application, and then play the game. After the chat time, only the wiser player has perfect information on the realized (random) sequence played by nature. The players then play the finitely repeated binary game. In treatment NC, subjects just play the game. In the experiment we observed endogenous communication treatment NC as well as exogenous in treatment C, both of which result in higher payoffs. Furthermore, when explicit communication is possible we observe a chat effect which can be interpreted as a higher level of efficiency in communication. Strategies used by subjects are in line with GHN strategies.
    Keywords: communication, transmission of information, efficiency, experiments
    JEL: D8 C91 C73
    Date: 2013
  4. By: Giuseppe Attanasi; Pierpaolo Battigalli; Elena Manzoni
    Abstract: In the theory of psychological games it is assumed that players' preferences on material consequences depend on endogenous beliefs. Most of the applications of this theoretical framework assume that the psychological utility functions representing such preferences are common knowledge. But this is often unrealistic. In particular, it cannot be true in experimental games where players are subjects drawn at random from a population. Therefore an incomplete-information methodology is called for. We take a first step in this direction, focusing on models of guilt aversion in the Trust Game. We consider two alternative modeling assumptions: (i) guilt aversion depends on the role played in the game, because only the trustee can feel guilt for letting the co-player down, (ii) guilt aversion is independent of the role played in the game. We show how the set of Bayesian equilibria changes as the upper bound on guilt sensitivity varies, and we compare this with the complete-information case. Our analysis illustrates the incomplete-information approach to psychological games and can help organize experimental results in the Trust Game.
    Keywords: Psychological games, Trust Game, guilt, incomplete information
    JEL: C72 C91 D03
    Date: 2013–06
  5. By: Abraham Neyman
    Abstract: We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage $k$, $k\geq 0$, of a stochastic game $\Gamma_\delta$ with stage duration $\delta$ is interpreted as the play in time $k\delta\leq t<(k+1)\delta$, and therefore the average payoff of the $n$-stage play per unit of time is the sum of the payoffs in the first $n$ stages divided by $n\delta$, and the $\lambda$-discounted present value of a payoff $g$ in stage $k$ is $\lambda^{k\delta} g$. We define convergence, strong convergence, and exact convergence of the data of a family $(\Gamma_\delta)_{\delta>0}$ as the stage duration $\delta$ goes to $0$, and study the asymptotic behavior of the value, optimal strategies, and equilibrium. The asymptotic analogs of the discounted, limiting-average, and uniform equilibrium payoffs are defined. Convergence implies the existence of an asymptotic discounted equilibrium payoff, strong convergence implies the existence of an asymptotic limiting-average equilibrium payoff, and exact convergence implies the existence of an asymptotic uniform equilibrium payoff.
    Date: 2013–04
  6. By: Hannes Rusch (University of Giessen); Max Albert (University of Munich)
    Abstract: In evolutionary models of indirect reciprocity, reputation mechanisms can stabilize cooperation even in severe cooperation problems like the prisoner’s dilemma. Under certain circumstances, conditionally cooperative strategies, which cooperate iff their partner has a good reputation, cannot be invaded by any other strategy that conditions behavior only on own and partner reputation. The first point of this paper is to show that an evolutionary version of backward induction can lead to a breakdown of this kind of indirectly reciprocal cooperation. Backward induction, however, requires trategies that count and then cease to cooperate in the last, last but one, last but two, game they play. These strategies are unlikely to exist in natural settings. We then present two new findings. (1) Surprisingly, the same kind of breakdown is also possible without counting. Strategies using rare golden opportunities for defection can invade conditional cooperators. This can create further golden opportunities, inviting the next wave of opportunists, and so on, until cooperation breaks down completely. (2) Cooperation can be stabilized against these opportunists, by letting an individual’s initial reputation be inherited from that individual’s parent. This ‘inclusive reputation’ mechanism can cope with any observably opportunistic strategy. Offspring of opportunists who successfully exploited a conditional cooperator cannot repeat their parents’ success because they inherit a bad reputation, which forewarns conditional cooperators in later generations.
    Keywords: evolutionary game theory; repeated prisoner’s dilemma; backward induction; conditional cooperation; opportunism;
    JEL: C73
    Date: 2013
  7. By: Oriol Tejada (ETH Zurich, Switzerland)
    Abstract: We consider a finitely populated economy in which there are different types of agent, each agent is of exactly one type, and profit is created by coalitions containing at most one agent of each type (or side). The surplus of a so-called generalized multisided assignment economy is defined as the maximum aggregate profit that can be attained by matching agents into pairwise disjoint coalitions of the above kind. We present negative results that establish that when the economy consists of more than two sides (i) agents on different sides may not be complements, i.e., they do not necessarily reinforce each other’s influence on the surplus and (ii) agents on the same side may not be substitutes, i.e., they do not necessarily interfere with each other’s influence on the surplus. These findings are in marked contrast with the results for two-sided assignment economies (Shapley, 1962). We propose novel notions for the complementarity and the substitutability of disjoint subsets of agents and we find conditions that ensure that the former are satisfied.
    Keywords: multisided assignment economy; complements; substitutes.
    JEL: C71 D40
    Date: 2013–05
  8. By: Klaus Eisenack (University of Oldenburg, Department of Economics); Leonhard Kähler
    Abstract: Policy advocates frequently request for unilateral action to push forward climate protection in international negotiations. It is yet conventional wisdom in environmental economics that unilateral action does not pay for the first mover due to free-riding behavior of the other countries. How does this analysis change if there is a further option at hand: off-setting damages from joint emissions by individual adaptation measures? Adaptation to climate change plays an increasingly role in the international negotiations under the UNFCCC. This paper shows that when adaptation is considered as an explicit decision variable, and unilateral action is framed as a Stackelberg game, the resulting convexity properties imply (when the follower has a specific property) that total emissions are reduced to the benefit of all countries in the game equilibrium. When countries play a game of timing in a period before emission and adaptation decisions – to determine who takes the role of the Stackelberg leader – it is shown that a country with this specific property indeed becomes the follower. The equilibrium of the overall game is Pareto superior to the non-cooperative Nash solution.
    Keywords: international environemental problems; climate change; Stackelberg<br>game; convexity
    Date: 2012–01
  9. By: Molina, José Alberto (University of Zaragoza); Gimenez-Nadal, Jose Ignacio (University of Zaragoza); Cuesta, José A. (University of Zaragoza); Garcia-Lazaro, Carlos (University of Zaragoza); Moreno, Yamir (University of Zaragoza); Sanchez, Angel (University of Zaragoza)
    Abstract: Charles Darwin (1874) stated that "women are less selfish but men are more competitive". Very recent papers (Eckel & Grossman, 1998, 2001 or Andreoni and Vesterlund 2001, among others) have shown the relevance of gender in altruism in both ultimatum and dictator games. In this paper we analyze the role of gender in repeated Prisoners' Dilemma played by Spanish high-school students in both a square lattice and a heterogeneous network. We find that female students have a higher probability of cooperation than male students.
    Keywords: high school students, cooperation, gender differences, prisoners' dilemma
    JEL: C72 C73 C93 D03 J16
    Date: 2013–05
  10. By: Philipp Möhlmeier (BiGSEM - Bielefeld University - Center for Mathematical Economics); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Emily Tanimura (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)
    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 co-author 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 degree-distance-based 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 degree-distance-based utility.
    Keywords: Connections model; degree; distance; negative externalities; positive externalities; pairwise stability; efficiency
    Date: 2013–04

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