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on Game Theory |
| By: | Britz Volker; Herings P. Jean-Jacques; Predtetchinski Arkadi (METEOR) |
| Abstract: | Our work contributes to the game-theoretic analysis of bargaining by providing additional non-cooperative support to the well-known Nash bargaining solution. In particular, in the present paper we study a model of non-cooperative multilateral bargaining with a very general proposer selection protocol and set of feasible payoffs. In each period of the bargaining game, one out of n players is recognized as the proposer according to an irreducible Markov process. The proposer offers a particular element of the convex set of feasible payoffs. If all players accept the offer, it is implemented. If a player rejects the offer, with some probability the negotiations break down and with the remaining probability the next period starts. We show that subgame perfect equilibria in stationary strategies exist and we fuly characterize the set of such equilibria. Our main result is that in the limit, as the exogenous risk of breakdown goes to zero, stationary subgame perfect equilibrium payoffs converge to the weighted Nash bargaining solution with the stationary distribution of the Markov proposer selection process as the weight vector. |
| Keywords: | operations research and management science; |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2008018&r=gth |
| By: | Sophie Bade; Guillaume Haeringer; Ludovic Renou |
| Abstract: | We consider non-cooperative environments in which two players have the power to commit but cannot sign binding agreements. We show that by committing to a set of actions rather than to a single action, players can implement a wide range of action profiles. We give a complete characterization of implementable profiles and provide a simple method to find them. Profiles implementable by bilateral commitments are shown to be generically inefficient. Surprisingly, allowing for gradualism (i.e., step by step commitment) does not change the set of implementable profiles. |
| Keywords: | Commitment; self-enforcing; generic inefficiency; agreements; Pareto-improvement |
| JEL: | C70 C72 H87 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:08/20&r=gth |
| By: | Peter Csoka (Department Economics, Universiteit of Maastricht); P. Jean-Jacques Herings, (Department of Economics, Universiteit Maastricht,); Laszlo A. Koczy (Department of Economics, Universiteit Maastricht,) |
| Abstract: | Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games. We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games. |
| Keywords: | Coherent Measures of Risk, Risk Allocation Games, Totally Balanced Games, Exact Games |
| JEL: | C71 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:0704&r=gth |
| By: | Joseph Abdou (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Ecole d'économie de Paris - Paris School of Economics - Université Panthéon-Sorbonne - Paris I); Hans Keiding (University of Copenhagen - Institute of Economics) |
| Abstract: | We introduce a description of the power structure which is inherent in a strategic game form using the concept of an interaction sheaf. The latter assigns to each open set of outcomes a set of interaction arrays, specifying the changes that coalitions can make if outcome belongs to this open set. The interaction sheaf generalizes the notion of effectivity functions which has been widely used in implementation theory, taking into consideration that changes in outcome may be sustained not only by single coalitions but possibly by several coalitions, depending on the underlying strategy choices. Also, it allows us to consider game forms with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding (2003). |
| Keywords: | Nash equilibrium, strong equilibrium, solvability, effectivity, acyclicity. |
| Date: | 2008–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00289299_v1&r=gth |
| By: | Kumagai, Satoru |
| Abstract: | Researchers have long believed the concept of "excitement" in games to be subjective and difficult to measure. This paper presents the development of a mathematically computable index that measures the concept from the viewpoint of an audience and from that of a player. One of the key aspects of the index is the differential of the probability of "winning" before and after one specific "play" in a given game. The index makes a large contribution to the study of games and enables researchers to compare and analyze the “excitement†of various games. It may be applied in many fields, especially the area of welfare economics, and applications may range from those related to allocative efficiency to axioms of justice and equity. |
| Keywords: | Game, Game system, Excitement, Mathematics |
| JEL: | C69 D63 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:jet:dpaper:dpaper157&r=gth |
| By: | Francesco Farina; Niall O'Higgins; Patrizia Sbriglia |
| Abstract: | The intention to “invest” in the Trust Game in extensive form revealed by a move could conceal different motivations. Whether the motive hidden beneath the manifest behaviour of the first mover is the desire to invest in a relationship of mutual advantage with the trustee or the desire to be good to him independently from his own final payoff, remains an unsettled question. The question then is how to identify the motive which is actually at work, out of the two possible motives embedded in the trust game: 1) an “investment” motive - conditional cooperation is a way to express the expectation of reciprocal behaviour; and/or, 2) an altruistic motive - what may appear as an “investment” actually conceals a social preferences, that is the intention to gratuitously favour the other player. In this paper we attempt to elicit the true motive underlying the behaviour of each of the two players and suggest that the most informative utilization of surveys in this regard goes beyond the simple comparison between answers to a questionnaire and actual behaviour. The statistical treatment of players’ behaviour in the sessions, by means of attitudes as shown by their answers, allows a deeper understanding of the players’ behaviour and a better evaluation of the experimental results. Therefore, the objective of disentangling the strategic motive (the intention of the trustor to elicit benevolence from the trustee, and the trustee interest in reciprocating) from the altruistic motive will be pursued by establishing a correlation between the attitudinal and the behavioural measures of trust and trustworthiness. In this paper, we will then be using the “words” of answers to a questionnaire in order to more deeply understand the motivations behind “actions”. |
| Keywords: | Experimental economics, Surveys, Trust, Reciprocity |
| JEL: | C42 C72 C91 D63 D64 D83 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:usi:labsit:021&r=gth |
| By: | Holmberg, Pär (Research Institute of Industrial Economics (IFN)) |
| Abstract: | Forward sales is a credible commitment to aggressive spot market bidding, and it mitigates producers’ market power in electricity markets. Still it can be profitable for a producer to make such a commitment if it results in a soft response from competitors in the spot market (strategies are substitutes). The optimal contracting level of a risk-neutral producer is determined by the extent to which strategies are substitutes and the slope of the residual demand in the forward market. Conditions under which strategies are substitutes are identified for a two-stage game with supply function competition and capacity constrained producers. |
| Keywords: | Supply Function Equilibrium; Forward Market; Strategic Contracting; Arbitrage; Strategic Substitutes; Oligopoly; Electricity Market |
| JEL: | C72 D43 D44 G13 L13 L94 |
| Date: | 2008–06–24 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:iuiwop:0756&r=gth |
| By: | Jing Li (Department of Economics, University of Pennsylvania) |
| Abstract: | This paper extends Li (2008b) to the multi-agent environment, where players reason about each other’s awareness as well as knowledge, subject to their own awareness constraints. I characterize the interactive knowledge hierarchies under unawareness, which significantly differ from those in the standard information partition model by allowing for false interactive knowledge. Aumann’s classic characterization of common knowledge does not immediately apply in this environment, even if there is “common awareness” of the event involved. An alternative characterization of common knowledge is provided. |
| Keywords: | unawareness, state space models, interactive knowledge, common knowledge |
| JEL: | C70 C72 D80 D82 D83 |
| Date: | 2008–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:08-023&r=gth |
| By: | Julio Davila (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Ecole d'économie de Paris - Paris School of Economics - Université Panthéon-Sorbonne - Paris I); Jan Eeckhout (University of Pennsylvania - Department of Economics); César Martinelli (Centro de Investigacion Economica - Instituto Tecnologico Autonomo) |
| Abstract: | In a simple public good economy, we propose a natural bargaining procedure whose equilibria converge to Lindahl allocations as the cost of bargaining vanishes. The procedure splits the decision over the allocation in a decision about personalized prices and a decision about output levels for the public good. Since this procedure does not assume price-taking behavior, it provides a strategic foundation for the personalized taxes inherent to the Lindahl solution to the public goods problem. |
| Keywords: | Public goods, bargaining, alternating offers. |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00289435_v1&r=gth |
| By: | Jing Li (Department of Economics, University of Pennsylvania) |
| Abstract: | I develop a set-theoretic model of unawareness without making any structural assumptions on the underlying state space. Unawareness is characterized as a measurability constraint that results in players' reasoning about a “coarse" subjective algebra of events. The model is shown to be essentially equivalent to the product model in Li (2007), indicating that such a measurability constraint can be captured by restrictions on the dimensions of the state space without loss of generality. I use a variant of the partition model to examine the case of partial unawareness, where the player is aware of a question but unaware of some possible answers to that question, and characterize the player's knowledge hierarchies from his subjective perspective. |
| Keywords: | unawareness, partial unawareness, information, information partition, the state space |
| JEL: | C70 C72 D80 D82 D83 |
| Date: | 2008–01–02 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:08-021&r=gth |
| By: | Jing Li (Department of Economics, University of Pennsylvania) |
| Abstract: | I study how choice behavior given unawareness of an event differs from choice behavior given subjective belief of zero probability on that event. Depending on different types of unawareness the decision-maker suffers, behavior under unawareness is either incomparable with that under zero probability (in the case of pure unawareness), or drastically different (in the case of partial unawareness). The key differences are (1) partial unawareness permits dynamically inconsistent choice, while zero probability beliefs do not; and (2) there are unforeseen options in an unawareness environment that are necessarily modeled as dominated options in zero probability models. |
| Keywords: | unawareness, zero probability, dynamic consistency, unforeseen contingency, unforeseen options |
| JEL: | C70 C72 D80 D82 D83 |
| Date: | 2008–01–02 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:08-022&r=gth |
| By: | Jing Li (Department of Economics, University of Pennsylvania) |
| Abstract: | I construct a state space model with unawareness following Aumann (1976). Dekel, Lipman and Rustichini (1998a) show that standard state space models are incapable of representing unawareness. The model circumvents the impossibility result by endowing the agent with a subjective state space that differs from the full state space when he has the unawareness problem. Information is modeled as a pair, consisting of both factual information and awareness information. The model preserves the central properties of the standard information partition model. |
| Keywords: | unawareness, information, information partition, state space models |
| JEL: | C70 C72 D80 D82 D83 |
| Date: | 2008–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:08-024&r=gth |
| By: | Xiao, Erte; Bicchieri, Cristina |
| Abstract: | Inequity aversion and reciprocity have been identified as two primary motivations underlying human decision making. However, because income and wealth inequality exist to some degree in all societies, these two key motivations can point to different decisions. In particular, when a beneficiary is less wealthy than a benefactor, a reciprocal action can lead to greater inequality. In this paper we report data from a trust game variant where trustees’ responses to kind intentions generate inequality in favor of investors. In relation to a standard trust game treatment where trustees’ responses reduce inequality, the proportion of non-reciprocal decisions is twice as large when reciprocity promotes inequality. Moreover, we find investors expect that this will be the case. Overall, although both motives clearly play a role, we found strong evidence for inequality aversion. Our results call attention to the potential importance of inequality in principal-agent relationships, and have important implications for designing policies aimed at promoting cooperation. |
| JEL: | D63 C72 C91 |
| Date: | 2008–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:9375&r=gth |
| By: | Quazi Shahriar (Department of Economics, San Diego State University) |
| Abstract: | Risk aversion and impatience of either the bidders or the seller have been utilized to explain the popularity of buy prices in private value auctions. This paper, using a pure common value framework, models auctions with “temporary” buy prices. We characterize equilibrium bidding strategies in a general setup and then analyze a seller’s incentive to post a buy price when there are two bidders. We find that, when bidders are either risk neutral or risk averse, a risk neutral seller has no incentive to post a buy price. But when the seller is risk averse, a suitably chosen buy price can raise his expected payoff when the bidders are either risk neutral or risk averse. This provides an explanation for the popularity of buy prices in online common value auctions. |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:sds:wpaper:0031&r=gth |
| By: | Pot Erik; Peeters Ronald; Peters Hans; Vermeulen Dries (METEOR) |
| Abstract: | We analyze whether noncooperative collusive equilibria are harder to sustain when individual demand levels are not fixed but are able to fluctuate. To do this, we extend a Bertrand type model of price competition to allow for fluctuating market shares when prices are equal. We find that, the larger the market share fluctuations may be, the higher the discount factor should be to sustain a collusive equilibrium in trigger strategies. The intuition behind this is fairly straightforward. When individual demand in the collusive state is suddenly low, the gains from collusion go down. Moreover, the firm with the low demand can capture a larger share of the market by deviating from the collusive strategy. The incentive to deviate therefore becomes larger when the individual market share decreases. We also look at the existence of a specific type of semi-collusive equilibrium when individual market shares are either common knowledge or private knowledge. We find that there exist equilibria in which competitive periods (price wars) occur with probability 1 and on the equilibrium path. |
| Keywords: | mathematical economics; |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2008017&r=gth |