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on Game Theory |
| By: | Kleppe, J.; Borm, P.E.M.; Hendrickx, R.L.P. (Tilburg University, Center for Economic Research) |
| Abstract: | Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium and show that the set of fall back equilibria is a non-empty and closed subset of the set of Nash equilibria. We discuss the relations with other equilibrium concepts, and among other results it is shown that each robust equilibrium is fall back and for bimatrix games also each proper equilibrium is a fall back equilibrium. Furthermore, we show that for bimatrix games the set of fall back equilibria is the union of finitely many polytopes, and that the notions of fall back equilibrium and strictly fall back equilibrium coincide. Finally, we allow multiple actions to be blocked, resulting in the notion of complete fall back equilibrium. We show that the set of complete fall back equilibria is a non-empty and closed subset of the set of proper equilibria. |
| Keywords: | strategic game;equilibrium refinement;blocked action;fall back equilibrium |
| JEL: | C72 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200831&r=gth |
| By: | Ciftci, B.B.; Borm, P.E.M.; Hamers, H.J.M. (Tilburg University, Center for Economic Research) |
| Abstract: | A highway problem is determined by a connected graph which provides all potential entry and exit vertices and all possible edges that can be constructed between vertices, a cost function on the edges of the graph and a set of players, each in need of constructing a connection between a specific entry and exit vertex. Mosquera and Zarzuelo (2006) introduce highway problems and the corresponding cooperative cost games called high- way games to address the problem of fair allocation of the construction costs in case the underlying graph is a chain. In this note, we study the concavity and the balancedness of highway games on more general graphs. A graph G is called highway-game concave if for each highway problem in which G is the underlying graph the corresponding highway game is concave. The main result of our study is that a graph is highway-game concave if and only if it is weakly triangular. Moreover, we provide sufficient conditions on highway problems defined on cyclic graphs such that the corresponding highway games are balanced. |
| Keywords: | cooperative games;highway games;cost sharing. |
| JEL: | C71 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200829&r=gth |
| By: | H. Peyton Young |
| Abstract: | A person learns by trial and error if he occasionally tries out new strategies, rejecting choices that are erroneous in the sense that they do not lead to higher payoffs. In a game, however, strategies can become erroneous due to a change of behavior by someone else. We introduce a learning rule in which behavior is condition on whether a player experiences an error of the first or second type. This rule, called interactive trial and error learning, implements Nash equilibrium behavior in any game with generic payoffs and at least one pure Nash equilibrium. |
| Keywords: | Learning, Adaptive Dynamics, Nash Equilibrium, Bounded Rationality |
| JEL: | C72 D83 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:384&r=gth |
| By: | Giacomo Calzolari; Alessandro Pavan |
| Abstract: | In games in which multiple principals contract simultaneously and non-cooperatively with the same agent, standard direct revelation mechanisms in which the agent reports his type(i.e. his exogenous private information) have been proven inadequate to characterize the entire set of equilibrium outcomes. This paper introduces a more general class of revelation mechanisms in which the agent reports also the contractual decisions he is inducing with the principals. We rst show that such a class has the same nice properties as the class of all unrestricted menus: (i) for any equilibrium of any indirect game with arbitrary communication space for the principals, there exists a truthful equilibrium in the game in which the principals are restricted to o¤er revelation mechanisms that sustains the same outcomes; (ii) any truthful equilibrium is robust in the sense that it remains an equilibrium in any game in which the principalsstrategy space is enlarged. We next show how revelation mechanisms can be put to work in applications such as menu auctions, moral hazard settings, and competition in non-linear tari¤s to identify necessary and su¢ cient conditions for the sustainability of outcomes as common agency equilibria. |
| Keywords: | mechanism design, contracts, Revelation Principle. |
| JEL: | D89 C72 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1458&r=gth |
| By: | Jason Shachat; J. Todd Swarthout |
| Abstract: | We examine experimentally how humans behave when they, unbeknownst to them, play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects' play was consistent with their Nash equilibrium strategy. But a larger percentage of subjects' play was more consistent with different models of play: equal-probable play for the zero-sum game, and the minimax strategy in the non-profitable game. |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:exc:wpaper:2008-07&r=gth |
| By: | Yannick Viossat (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX) |
| Abstract: | The dual reduction process, introduced by Myerson, allows to reduce a finite game into a smaller dimensional game such that any equilibrium of the reduced game is an equilibrium of the original game. This holds both for Nash equilibrium and correlated equilibrium. We present examples of applications of dual reduction and argue that this is a useful tool to study Nash equilibria and correlated equilibria. We then investigate its properties. |
| Keywords: | correlated equilibrium, Nash equilibrium, dual reduction |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:hal-00264031_v1&r=gth |
| By: | Hannah Hörisch (University of Munich); Oliver Kirchkamp (University of Jena, School of Economics) |
| Abstract: | We use experiments to compare dynamic and static wars of attrition (i.e. second-price all-pay auctions) and first-price all-pay auctions. Many other studies find overbidding in first-price all-pay auctions. We can replicate this property. In wars of attrition, however, we find systematic underbidding. We study bids and revenue in different experimental frames and matching procedures and draw a link to the literature on stepwise linear bidding functions. |
| Keywords: | War of attrition, dynamic bidding, all-pay auction, stabilisation, volunteer's dilemma, experiment |
| JEL: | C72 C92 D44 E62 H30 |
| Date: | 2008–03–18 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2008-023&r=gth |
| By: | Oliver Kirchkamp (University of Jena, School of Economics); Eva Poen (University of Nottingham); J. Philipp Reiß (Maastricht University, Economics Department) |
| Abstract: | In this paper we study equilibrium- and experimental bidding behaviour in ?rst-price and second price auctions with outside options. We ?nd that bidders do respond to outside options and to variations of common knowledge about competitors' outside options. However, overbidding in ?rst-price auctions is signi?cantly higher with outside options than without. First-price auctions yield more revenue than second-price auctions. This revenue-premium is signi?cantly higher with outside options. In second-price auctions the introduction of outside options has only a small effect. |
| Keywords: | Experiments, Auction, Expectations |
| JEL: | C92 D44 |
| Date: | 2008–02–18 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2008-022&r=gth |
| By: | Eddie Dekel; Matthew Jackson; Asher Wolinsky |
| Abstract: | We study all-pay auctions (or wars of attrition), where the highest bidder wins an object, but all bidders pay their bids. We consider such auctions when two bidders alternate in raising their bids and where all aspects of the auction are common knowledge including biddersvaluations. We analyze how the ability to jump-bid, or raise bids by more than the minimal necessary increment a¤ects the outcome of the auction. We also study the impact of budget caps on total bids. We show that both of these features, which are common in practice but absent from the previous literature, matter signi cantly in determining the outcome of the auctions. |
| Keywords: | All-Pay Auctions, Jump-Bidding, Auctions, War of Attrition. |
| JEL: | C62 C63 C72 D44 D82 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1454&r=gth |
| By: | Holm, Håkan J. (Department of Economics, Lund University) |
| Abstract: | Beliefs in signals that reveal lies or truths are widespread. These signals may lead to a truth or lie detection bias if the probability that such a signal is perceived by the receiver is contingent on the truth value of the sender’s message. Such detection biases are analyzed theoretically in a bluffing game. The detection bias shrinks the equilibrium set to a unique non-pooling equilibrium, in which the better a player is at detecting lies the more often the opponent player will lie. With proper deception techniques such biases can in principle be used to extract hidden information. |
| Keywords: | Bluffing; Game theory; Truth detection; Lie detection; Detection bias |
| JEL: | C72 D82 |
| Date: | 2008–02–29 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2008_004&r=gth |
| By: | Holm, Håkan J. (Department of Economics, Lund University); Kawagoe, Toshiji (Department of Complex Systems) |
| Abstract: | This paper investigates face-to-face lying and beliefs associated with it. In experiments in Sweden and Japan, subjects answer questions about personal characteristics, play a face-to-face sender-receiver game and participate in an elicitation of lie-detection beliefs. The previous finding of too much truth-telling (compared to the equilibrium prediction) also holds in the face-to-face setting. A new result is that although many people claim that they are good at lie-detection, few reveal belief in this ability when money is at stake. Correlations between the subjects’ characteristics and their behavior and performances in the game are also explored. |
| Keywords: | Lying; Game theory; Truth detection; Lie-detection; Experiment |
| JEL: | C72 C91 D82 |
| Date: | 2008–02–29 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2008_005&r=gth |
| By: | Olivier Gossner; Ehud Kalai; Robert Weber |
| Abstract: | Conditions of information independence are important in information economics and game theory. We present notions of partial independence in Bayesian environments, and study their relationships to notions of common knowledge. |
| Keywords: | Bayesian games, independent types, common knowledgees |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1453&r=gth |
| By: | Oliver Kirchkamp (University of Jena, School of Economics); J. Philipp Reiß (Maastricht University, Economics Department); Abdolkarim Sadrieh (University of Magdeburg, Faculty of Economics and Management) |
| Abstract: | We introduce a new method of varying the risk that bidders face in first-price private value auctions. We find that decreasing bidders' risk significantly reduces the degree of overbidding relative to the risk-neutral Bayesian-Nash equilibrium prediction. This implies that risk a?ects bidding behavior as generally expected in auction theory. While resolving a long-standing debate on the e?ect of risk on auction behavior, our results give rise to a new puzzle. As risk is diminished and overbidding decreases for most of the value range, a significant degree of underbidding sets in for very low values. |
| Keywords: | risk, fist-price auctions, risk-aversion, overbidding |
| JEL: | C92 D44 |
| Date: | 2008–03–19 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2008-024&r=gth |
| By: | Giacomo Calzolari; Alessandro Pavan |
| Abstract: | This paper considers dynamic games in which multiple principals contract sequentially and non-cooperatively with the same agent and provides characterization results useful for applications. Our benchmark model is one of private contracting in which downstream principals do not observe upstream mechanisms, nor the decisions taken in these mechanisms. We show that any equilibrium outcome that can be sustained with any arbitrary strategy space for the principals can also be sustained by restricting the principals to offer excended direct mechanisms. In these mechanisms, the agent first reports his extended type (i.e. his exogenous private information along with the endogenous payoff-relevant decisions contracted upstream), the principal then responds by offering the agent a (possibly degenerate) menu of contracts that are payoff-equivalent for that extended type, and finally the agent selects a contract from this menu and the contract is executed. We also show that characterizing equilibria through extended direct mechanisms is facilitated by the fact that (i) each principal can be restricted to offer a single mechanism; (ii) when the agent's strategy is Markov (i.e. it depends only on payoff-relevant information), each mechanism can be restricted to offer a single contract to each extended type; and (iii) restricting the agent's strategy to be Markov is without loss in the case of deterministic decisions, e.g. when the contracts are deterministic and the agent does not mix over effort. We finally show how the aforementioned results must be adjusted to occommodate alternative assumptions on the observability of upstream histories and/or the sequence of contracting examined in the literature. |
| Keywords: | Sequential common agency, mechanism design, contracts, endogenous types. |
| JEL: | D82 C73 L1 |
| Date: | 2007–04 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1457&r=gth |
| By: | Tom Truyts |
| Abstract: | How do incentives to engage in costly signaling depend on social structure? This paper formalises and extends Thorstein Veblen’s theory of how costly signaling by conspicuous consumption depends on social structure. A noisy signaling game is introduced in which spectators observe signals only imperfectly, and use Bayesian updating to interpret the observed signals. It is shown that this noisy signaling game has (under some weak regularity conditions) a unique plausible Perfect Bayesian Nash equilibrium. Then, a social information network is introduced as a second source of information about a player’s type. Equilibrium signaling depends in the resulting game on the relative quality of the substitute sources of information, which depends again on the social network. For some highly stylised networks, the dependence of equilibrium costly signaling on network characteristics (network size, density and connectedness, the centrality of the consumer in the network) is studied, and a simple dominance result for more arbitrary networks is suggested. |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:ete:ceswps:ces0719&r=gth |
| By: | Oliver Kirchkamp (University of Jena, School of Economics); J. Philipp Reiß (Maastricht University, Economics Department) |
| Abstract: | Deviations from equilibrium bids in auctions can be related to inconsistent expectations with correct best replies (see Eyster and Rabin, 2005; Crawford and Iriberri, 2007) or correct expectations but small (perhaps quantal-response) mistakes in best replies (see Goeree et al., 2002). To distinguish between these two explanations we use a novel experimental procedure and study expectations together with best replies. We extensively test the internal validity of this setup. We ?nd that deviations from equilibrium bids do not seem to be due to wrong expectations but due to deviations from a best reply. |
| Keywords: | Experiments, Auction, Expectations |
| JEL: | C92 D44 |
| Date: | 2008–03–18 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2008-021&r=gth |
| By: | Tavoni, Alessandro |
| Abstract: | Substantial evidence has been accumulated in recent empirical works on the limited ability of the Nash equilibrium to rationalize observed behavior in many classes of games played by experimental subjects. This realization has led to several attempts aimed at finding tractable equilibrium concepts which perform better empirically, often by introducing a reference point to which players compare the available payoff allocations, as in impulse balance equilibrium (Selten & Chmura, forthcoming) and in the inequity aversion model (Fehr & Schmidt,1999). The purpose of this paper is to review some features of this recent literature and to propose a new, empirically sound, unifying concept which combines elements of fairness with reference considerations. |
| Keywords: | Fairness; Inequity aversion; Aspiration level; Impulse balance; Behavioral economics; Experimental economics; Jacknife estimator |
| JEL: | D63 D01 C72 C91 |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:7760&r=gth |
| By: | Bard Harstad |
| Abstract: | I investigate when a exible bargaining agenda, where side payments are possible, facilitates cooperation in a context with strategic delegation. On the one hand, allowing side payments may be necessary when one partys participation constraint otherwise would be violated. On the other, with side payments each principal appoints a delegate that values the project less, since this increases her bargaining power. Reluctant agents, in turn, implement too few projects. I show that side payments are bad if the heterogeneity is small while the uncertainty and the typical value of the project are large. With a larger number of parties there may be a stalemate without side payments, but delegation becomes more strategic as well, and cooperation decreases in either case. |
| Keywords: | Collective action, side transfers, bargaining agenda, strategic delegation, issue linkages |
| JEL: | C78 D78 F53 H77 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1452&r=gth |
| By: | Jung, Hanjoon Michael |
| Abstract: | In an information transmission situation, a sender's concern for its credibility could endow itself with an invisible power to control the receiver's decisions so that the sender can manipulate information without being detected. In this case, the sender can achieve its favored outcome without losing its credibility, which stays true even when the sender and the receiver have contradictory preferences. Therefore, the sender's concern for its credibility could result in less truthful signals from the sender and worse payoffs to the receiver. This is the paradox of credibility. This paper models this paradoxical role of the sender's credibility concern. |
| Keywords: | Anti-coordination game; Credibility; Information Transmission;Hawk-Dove game; Paradox. |
| JEL: | D82 D83 C72 |
| Date: | 2008–03–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:7443&r=gth |
| By: | Noemí Navarro (Department of Economic Theory, Universidad de Málaga) |
| Abstract: | This paper takes an axiomatic approach for allocating the value of a network when the externalities generated across components are identifiable. Two main approaches exist up to my knowledge: Myerson's (1977) and Jackson's (2005), where the fairness and the flexible network axioms were defined, respectively. I first characterize the Myerson value in terms of the axioms de?ned by Jackson (2005) and then I revisit the flexible network approach by taking into account the distribution of the total value of a network among its components. Two new, and different, allocation rules are defined and characterized in this context, both collapsing into the player-based flexible-network allocation rule in the absence of externalities. I further suggest a flexible network approach from a component-wise point of view, giving it a flavor of stability, and define and characterize a new allocation rule. To conclude, I put all these allocation rules in perspective with respect to the notion of fairness as understood by Myerson (1977). |
| Keywords: | Myerson value, flexible-network approach, allocation rules, networks |
| JEL: | C71 C79 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:mal:wpaper:2008-2&r=gth |
| By: | Pablo Amoros (Department of Economic Theory, Universidad de Málaga) |
| Abstract: | The unequivocal majority of a social choice rule F is the minimum number of agents that must agree on their best alternative in order to guarantee that this alternative is the only one prescribed by F. If the unequivocal majority of F is larger than the minimum possible value, then some of the alternatives prescribed by F are undesirable (there exists a different alternative which is the most preferred by more than 50% of the agents). Moreover, the larger the unequivocal majority of F, the worse these alternatives are (since the proportion of agents that prefer the same different alternative increases). We show that the smallest unequivocal majority compatible with Maskin-monotonicity is n-((n-1)/m), where n=3 is the number of agents and m=3 is the number of alternatives. This value represents no less than 66.6% of the population. |
| Keywords: | Maskin-monotonicity; Majority; Condorcet winner |
| JEL: | C70 D78 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:mal:wpaper:2008-3&r=gth |
| By: | Tessa Bold |
| Abstract: | This paper models the implications of endogenous group formation for efficient risk-sharing contracts in the dynamic limited commitment model. Endogenising group formation requires that any risk-sharing arrangement is not only stable with respect to individual deviations but also with respect to deviations by sub-groups. This requirement alters the central predictions of the dynamic limited commitment model for efficient bilateral risk-sharing. Firstly, consumption of constrained agents depends on the previous history of shocks and the interaction of the history of shocks with the current income realizations of other constrained agents. As a consequence, the efficient contract does not display amnesia. Secondly, the covariance between current consumption and past income can take on negative values. Based on the first result, we derive a formal test for the presence of endogenous group formation under limited commitment. In addition, we show how this test can be extended to distinguish a limited commitment/perfect information environment from a full commitment/imperfect information environment empirically. |
| Keywords: | Risk-Sharing, Limited Commitment, Endogenous Group Formation |
| JEL: | D02 D86 C72 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:387&r=gth |
| By: | H. Peyton Young |
| Abstract: | A person is concerned about self-image if his utility function depends, not only on his actions, but also on his beliefs about what sort of person he is. This dual motivation problem makes it difficult, and in some cases impossible, for someone to learn who he really is based solely on his revealed behavior. Indeed, there are very simple situations, involving just two actions and two possible identities, such that, if there is any initial uncertainty about one's true identity, it will never be resolved even when one has an infinite number of opportunities to act. |
| Keywords: | Knowledge, Self-Signalling, Learning |
| JEL: | C70 D83 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:383&r=gth |