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on Game Theory |
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Issue of 2011‒08‒29
nineteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Martimort, David; Stole, Lars |
| Abstract: | An aggregate game is a normal-form game with the property that each player’s payoff is a function only of his own strategy and an aggregate function of the strategy profile of all players. Aggregate games possess a set of purely algebraic properties that can often provide simple characterizations of equilibrium aggregates without first requiring that one solves for the equilibrium strategy profile. The defining nature of payoffs in an aggregate game allows one to project the n-player strategic analysis of a normal form game onto a lower-dimension aggregate-strategy space, thereby converting an n-player game to a simpler object – a self-generating single-person maximization program. We apply these techniques to a number of economic settings including competition in supply functions and multi-principal common agency games with nonlinear transfer functions. |
| Keywords: | Aggregate games; common agency; asymmetric informa- tion; menu auctions |
| JEL: | D8 C72 |
| Date: | 2011–06–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:32871&r=gth |
| By: | Jaume García Segarra (Fundamentos del Análisis Económico (Economics Department), Universitat Jaume I); Miguel Ginés Vilar (Fundamentos del Análisis Económico (Economics Department), Universitat Jaume I) |
| Abstract: | We propose and characterize a new solution for problems with asymmetric bargaining power among the agents that we named weighted proportional losses solution. It is specially interesting when agents are bargaining under restricted probabilistic uncertainty. The weighted proportional losses assigns to each agent losses proportional to her ideal utility and also proportional to her bargaining power. This solution is always individually rational, even for 3 or more agents and it can be seen as the normalized weighted equal losses solution. When bargaining power among the agents is equal, the weighted proportional losses solution becomes the Kalai-Smorodinsky solution. We characterize our solution in the basis of restricted monotonicity and restricted concavity. A consequence of this result is an alternative characterization of Kalai-Smorodinsky solution which includes contexts with some kind of uncertainty. Finally we show that weighted proportional losses solution satisfyies desirable properties as are strong Pareto optimality for 2 agents and continuity also fulfilled by Kalai-Smorodinsky solution, that are not satisfied either by weighted or asymmetric Kalai-Smorodinsky solutions. |
| Date: | 2011–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:gra:wpaper:10/21&r=gth |
| By: | Giovanna Devetag; Francesca Pancotto; Thomas Brenner |
| Abstract: | In minority games, players in a group must decide at each round which of two available options to choose, knowing that only subjects who picked the minority op- tion obtain a positive reward. Previous experiments on the minority and similar congestion games have shown that players interacting repeatedly are remarkably able to coordinate eciently, despite not conforming to Nash equilibrium behavior. We conduct an experiment on a minority-of-three game in which each player is a team composed by three subjects. Each team can freely discuss its strategies in the game and decisions must be made via a majority rule. Team discussions are recorded and their content analyzed to detect evidence of strategy co-evolution among teams playing together. Our main results of team discussion analysis show no evidence sup- porting the mixed strategy Nash equilibrium solution, and support a low-rationality, backward-looking approach to model behavior in the game, more consistent with reinforcement learning models than with belief-based models. Showing level-2 ratio- nality (i.e., reasoning about others' beliefs) is positively and signicantly correlated with higher than average earnings in the game, showing that a mildly sophisticated approach pays off. In addition, teams that are more successful tend to become more egocentric over time, paying more attention to their own past successes than to the behavior of other teams. Finally, we nd evidence of mutual adaptation over time, as teams that are more strategic (i.e., they pay more attention to other teams' moves) induce competing teams to be more egocentric instead. Our results contribute to the understanding of coordination dynamics resting on heterogeneity and co-evolution of decision rules rather than on conformity to equilibrium behavior. In addition, they provide support at the decision process level to the validity of modeling behavior using low-rationality reinforcement learning models. |
| Keywords: | coordination, minority game, market eciency, information, self-organization, reinforcement learning s |
| JEL: | C72 C91 C92 |
| Date: | 2011–08–22 |
| URL: | http://d.repec.org/n?u=RePEc:ssa:lemwps:2011/18&r=gth |
| By: | Bolle, Friedel; Breitmoser, Yves; Otto, Philipp E. |
| Abstract: | This paper proposes two generalization of the core and evaluates them on experimental data of assignment games (workers and firms negotiate wages and matching). The generalizations proposed allow for social utility components (e.g. altruism) and random utility components (e.g. logistic perturbations). These generalizations are well-established in analyses of non-cooperative games, and they prove to be both descriptive and predictive in the assignment games analyzed here. The "logit core" allows us to define a "stochastically more stable" relation on the outcome set, which has intuitive implications, and it fits better than alternative approaches such as random behavior cores and regression modeling. |
| Keywords: | cooperative games; core; random utility; social preferences; laboratory experiment |
| JEL: | C71 C90 D64 |
| Date: | 2011–08–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:32918&r=gth |
| By: | John Duggan (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158) |
| Abstract: | This paper takes up the foundational issue of existence of stationary subgame perfect equi- libria in a general class of coalitional bargaining games that includes many known bargaining models and models of coalition formation. General sufficient conditions for existence of equilib- ria are currently lacking in many interesting environments: bargaining models with non-concave stage utility functions, models with a Pareto optimal status quo alternative and heterogeneous discount factors, and models of coalition formation in public good economies with consumption lower bounds. This paper establishes existence of stationary equilibrium under compactness and continuity conditions, without the structure of convexity or comprehensiveness used in the extant literature. The proof requires a precise selection of voting equilibria following different proposals. The result is applied to obtain equilibria in models of bargaining over taxes, coalition formation in NTU environments, and collective dynamic programming problems. |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:roc:wallis:wp62&r=gth |
| By: | Martimort, David; Stole, Lars |
| Abstract: | This note uses techniques developed for aggregate games to characterize the set of equilib- ria for a beauty contest or prediction game in which the experts’ preferences are quadratic, but with an otherwise unrestricted information structure for private signals and the state variable. We show that, on aggregate, the experts’ collective estimate of the unknown parameter to be estimated is unbiased for every equilibrium. |
| Keywords: | Aggregate games; beauty contests; prediction games |
| JEL: | C8 C72 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:32872&r=gth |
| By: | Martimort, David; Stole, Lars |
| Abstract: | We study games of public delegated common agency under asymmetric information. Us- ing tools from non-smooth analysis and optimal control, we derive best responses and characterize equilibria (both continuous and discontinuous) using self-generating opti- mization programs of which any equilibrium allocation must be a solution. Special atten- tion is given to common agency games in which each principal’s payoff is a linear function of the agent’s action. In such games the self-generating optimization program reduces to the maximization of the principals’ “aggregate” virtual surplus in which the agent’s marginal valuation is replaced by a confluence of “virtual” valuations that reflect com- mon agency problems. One noteworthy subset of equilibrium allocations are “virtually truthful” which are the incomplete-information generalization of Bernheim and Whin- ston’s (1986) “truthful” equilibria. Virtually-truthful equilibria are simple to calculate and illustrate two distinct sources of equilibrium distortion: inefficient contracting by a given coalition of active principals and inefficient participation (insufficient activity) by principals. Our results are illustrated by means of two games: a public goods game in which each player simultaneously offers a menu contract to a common provider of the public good in order to induce greater supply, and a lobbying game between conflicting interest groups in which each group offers a menu of contributions to a common political decision-maker in an attempt to influence policymaking. |
| Keywords: | Common agency; asymmetric information; menu auctions; delegated contracting games; public goods; lobbying; non-smooth analysis; non-smooth control |
| JEL: | D73 D8 C61 C72 |
| Date: | 2011–08–17 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:32874&r=gth |
| By: | Christian Rusche |
| Abstract: | The direct evolutionary approach according to Leininger (2003) states that players in a two player Tullock rent-seeking contest within a fi nite population behave „as if“ they were relative payoff maximizers. Accordingly contest expenditures are higher than in Nash equilibrium. The indirect evolutionary approach also predicts more aggressive behavior by the players since negatively interdependent preferences are evolutionary stable. Both players are willing to harm themselves in material terms just to harm their opponent even more. I consider that every player in the contest has to contract a delegate either using a relative contract or a no-win-nopay contract. I show that delegation once introduced is able to overcompensate all negative eff ects of negatively interdependent objective functions. But as in the case without delegation a commitment on more aggressive behavior is a dominant strategy. Nevertheless delegation endows principals with a material payoff that is equal to the payoff an individualistic player facing another individualistic player would get. |
| Keywords: | Contest; strategic delegation; spite; agency theory |
| JEL: | C72 D72 M52 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:rwi:repape:0270&r=gth |
| By: | Theodoros M. Diasakos; Kostas Koufopoulos |
| Abstract: | This paper revisits the problem of adverse selection in the insurance market of Rothschild and Stiglitz (1976). We propose a simple extension of the game-theoretic structure in Hellwig (1987) under which Nash-type strategic interaction between the informed customers and the uninformed firms results always in a particular separating equilibrium. The equilibrium allocation is unique and Pareto-efficient in the interim sense subject to incentive-compatibility and individual rationality. In fact, it is the unique neutral optimum in the sense of Myerson (1983). |
| Keywords: | Insurance Market; Adverse Selection; Incentive Efficiency |
| JEL: | D86 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:215&r=gth |
| By: | Gilles, R.P.; Lazarova, E.A.; Ruys, P.H.M. (Tilburg University, Center for Economic Research) |
| Abstract: | We consider a network economy in which economic agents are connected within a structure of value-generating relationships. Agents are assumed to be able to participate in three types of economic activities: autarkic self-provision; binary matching interactions; and multi-person cooperative collaborations. We introduce two concepts of stability and provide sufficient and necessary conditions on the prevailing network structure for the existence of stable assignments, both in the absence of externalities from cooperation as well as in the presence of size-based externalities. We show that institutional elements such as the emergence of socioeconomic roles and organizations based on hierarchical leadership structures are necessary for establishing stability and as such support and promote stable economic development. |
| Keywords: | Cooperatives;Networks;Clubs;Network economies;Stable matchings. |
| JEL: | C72 D71 D85 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2011084&r=gth |
| By: | John Duggan (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158) |
| Abstract: | This paper covers the theory of the uncovered set used in the literatures on tournaments and spatial voting. I discern three main extant definitions, and I introduce two new concepts that bound exist- ing sets from above and below: the deep uncovered set and the shallow uncovered set. In a general topological setting, I provide relationships to other solutions and give results on existence and external stability for all of the covering concepts, and I establish continuity properties of the two new uncovered sets. Of note, I characterize each of the uncovered sets in terms of a decomposition into choices from externally stable sets; I define the minimal generalized covering solution, a nonempty refinement of the deep uncovered set that employs both of the new relations; and I define the acyclic Banks set, a nonempty generalization of the Banks set. |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:roc:wallis:wp63&r=gth |
| By: | Noritsugu Nakanishi (Graduate School of Economics, Kobe University) |
| Abstract: | Taking account of the farsightedness of the countries and adopting the von Neumann-Morgenstern (vNM) stable set as the solution concept, we examine an FTA network formation game. FTA networks are represented by undirected graphs with their vertex sets being identified with the set of the countries. Each countryfs welfare depends upon the shape of the graph and its location in that graph. We examine two extreme cases: one in which the pre-agreement taris are very high and the other in which they are su- ciently low. In the former, the farsighted vNM stable set only supports global free trade, implying that bilateral FTAs are building blocks for achieving global free trade. In the latter, the farsighted vNM stable set does not support global free trade, instead it supports some inecient FTA networks, implying that bilateral FTAs are stumbling blocks against achieving global free trade. |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:koe:wpaper:1114&r=gth |
| By: | Anita Gantner; Wolfgang Höchtl; Rupert Sausgruber |
| Abstract: | This paper studies the vulnerability of the pivotal mechanism with respect to manipulation by groups. In a lab experiment, groups decide on the implementation of various alternatives, some of which imply opposite interests for the two subgroups. We investigate the occurrence of tacit and explicit collusion by allowing for communication within subgroups in one treatment and prohibiting it in another. Even though all agents' preferences are common knowledge and there exists a simple symmetric collusive strategy for one subgroup, we find little evidence for tacit collusion, not even with increasing experience. Only when explicit communication is allowed, collusion is established, and it becomes even more pronounced over time. |
| Keywords: | Collective Decision Making, Pivotal Mechanism, Collusion |
| JEL: | D71 D61 C92 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2011-15&r=gth |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Stephen Morris (Dept. Economics, Princeton University) |
| Abstract: | This essay is the introduction for a collection of papers by the two of us on "Robust Mechanism Design" to be published by World Scientific Publishing. The appendix of this essay lists the chapters of the book. The objective of this introductory essay is to provide the reader with an overview of the research agenda pursued in the collected papers. The introduction selectively presents the main results of the papers, and attempts to illustrate many of them in terms of a common and canonical example, the single unit auction with interdependent values. In addition, we include an extended discussion about the role of alternative assumptions about type spaces in our work and the literature, in order to explain the common logic of the informational robustness approach that unifies the work in this volume. |
| Keywords: | Mechanism design, Robust mechanism design, Common knowledge, Universal type space, Interim equilibrium, Ex post equilibrium, Dominant strategies, Rationalizability, Partial implementation, Full implementation, Robust implementation |
| JEL: | C79 D82 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1818&r=gth |
| By: | Silvana Krasteva; Huseyin Yildirim |
| Abstract: | This paper investigates the sequencing choice of a buyer who negotiates with the sellers of two complementary objects with uncertain payoffs. We show that the sequencing matters to the buyer only when equilibrium trade can be inefficient. In this case, the buyer begins with the less powerful seller if the sellers have sufficiently diverse bargaining powers. If, however, both sellers are strong bargainers, then the buyer begins with the stronger of the two. For either choice, the buyer’s sequencing (weakly) increases the social surplus. Our analysis further reveals that it is sometimes optimal for the buyer to raise her own cost of acquisition to better manage the supplier competition. As such, we find that the buyer may commit to paying the sellers a minimum price strictly above the marginal cost; and that the buyer may outsource an input even though it can be made in-house. Finally, we identify the first - and second - mover advantages in negotiations for the sellers. |
| Keywords: | negotiation, sequencing, bargaining power, coordination |
| JEL: | C70 L23 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:duk:dukeec:11-17&r=gth |
| By: | Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); Anastasios Koukoumelis (Max Planck Institute of Economics, Strategic Interaction Group); M. Vittoria Levati (Max Planck Institute of Economics, Strategic Interaction Group) |
| Abstract: | We compare, on the basis of a procedurally fair "provision point" mechanism, bids for a public project from which some gain and some lose with bids for a less efficient public project from which all gain. In the main treatment, participants independently decide which one, if any, of the public projects should be implemented. We also run control treatments where only one of the two projects can be implemented. We find that (a) mixed feelings per se do not affect bidding behavior, and (b) the provision frequency of the project that raises mixed feelings declines significantly when it faces competition from the public good. |
| Keywords: | Public project, Bidding behavior, Procedural fairness |
| JEL: | C72 C92 D63 H44 |
| Date: | 2011–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2011-034&r=gth |
| By: | James Andreoni; Charles Sprenger |
| Abstract: | There is convincing experimental evidence that Expected Utility fails, but when does it fail, how severely, and for what fraction of subjects? We explore these questions using a novel measure we call the uncertainty equivalent. We find Expected Utility performs well away from certainty, but fails near certainty for about 40% of subjects. Comparing non-Expected Utility theories, we strongly reject Prospect Theory probability weighting, we support disappointment aversion if amended to allow violations of stochastic dominance, but find the u-v model of a direct preference for certainty the most parsimonious approach. |
| JEL: | D81 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:17342&r=gth |
| By: | Soohyung Lee; Muriel Niederle; Hye-Rim Kim; Woo-Keum Kim |
| Abstract: | The large literature on costly signaling and the somewhat scant literature on preference signaling had varying success in showing the effectiveness of signals. We use a field experiment to show that even when everyone can send a signal, signals are free and the only costs are opportunity costs, sending a signal increases the chances of success. In an online dating experiment, participants can attach “virtual roses” to a proposal to signal special interest in another participant. We find that attaching a rose to an offer substantially increases the chance of acceptance. This effect is driven by an increase in the acceptance rate when the offer is made to a participant who is less desirable than the proposer. Furthermore, participants endowed with more roses have more of their offers accepted than their counterparts. |
| JEL: | C78 C93 J0 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:17340&r=gth |
| By: | Daron Acemoglu; Georgy Egorov; Konstantin Sonin |
| Abstract: | When voters fear that politicians may have a right-wing bias or that they may be influenced or corrupted by the rich elite, signals of true left-wing conviction are valuable. As a consequence, even a moderate politician seeking reelection chooses “populist’ policies - i.e., policies to the left of the median voter - as a way of signaling that he is not from the right. Truly right-wing politicians respond by choosing more moderate, or even left-of-center policies. This populist bias of policy is greater when the value of remaining in office is higher for the politician; when there is greater polarization between the policy preferences of the median voter and right-wing politicians; when politicians are indeed more likely to have a hidden right-wing agenda; when there is an intermediate amount of noise in the information that voters receive; when politicians are more forward-looking; and when there is greater uncertainty about the type of the incumbent. We show that similar results apply when some politicians can be corrupted or influenced through other non-electoral means by the rich elite. We also show that ‘soft term limits’ may exacerbate, rather than reduce, the populist bias of policies. |
| JEL: | C71 D71 D74 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:17306&r=gth |