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on Game Theory |
| By: | Andersson, O.; Argenton, C.; Weibull, J. (Tilburg University, Center for Economic Research) |
| Abstract: | We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share. |
| Keywords: | Nash equilibrium;refinement;strategic uncertainty;price competition;Bertrand competition;bargaining;Nash demand game |
| JEL: | C72 D43 L13 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:201070&r=gth |
| By: | Engwerda, J.C.; Salmah, Y. (Tilburg University, Center for Economic Research) |
| Abstract: | In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium. |
| Keywords: | linear-quadratic games;linear feedback Nash equilibrium;affine systems;solvability conditions;Riccati equations. |
| JEL: | C61 C72 C73 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:201079&r=gth |
| By: | Engwerda, J.C.; Salmah, Y. (Tilburg University, Center for Economic Research) |
| Abstract: | In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon. The performance function is assumed to be indefinite and the underlying system affine. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium. |
| Keywords: | linear-quadratic games;linear feedback Nash equilibrium;affine systems;solvability conditions;Riccati equations. |
| JEL: | C61 C72 C73 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:201078&r=gth |
| By: | Geir B. , Asheim (Dept. of Economics, University of Oslo); Voorneveld, Max (Department of Economics, Stockholm School of Economics); W. Weibull, Jörgen (Department of Economics, Stockholm School of Economics) |
| Abstract: | This paper provides a definition of epistemic stability of sets of strategy profiles,and uses it to characterize variants of curb sets in finite games, including the set of rationalizable strategies and minimal curb sets. |
| Keywords: | Epistemic game theory; epistemic stability; rationalizability; closedness under rational behavior; mutual p-belief |
| JEL: | C72 D83 |
| Date: | 2009–12–07 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:osloec:2010_001&r=gth |
| By: | Johannes Horner (Cowles Foundation, Yale University); Massimo Morelli (Columbia University & European University Institute); Francesco Squintani (Essex University) |
| Abstract: | This paper brings mechanism design to the study of conflict resolution in international relations. We determine when and how unmediated communication and mediation reduce the ex ante probability of conflict, in a simple game where conflict is due to asymmetric information. Unmediated communication helps reducing the chance of conflict as it allows conflicting parties to reveal their types and establish type-dependent transfers to avoid conflict. Mediation improves upon unmediated communication when the intensity of conflict is high, or when asymmetric information is large. The mediator improves upon unmediated communication by not precisely reporting information to conflicting parties, and precisely, by not revealing to a player with probability one that the opponent is weak. Surprisingly, in our set up, arbitrators who can enforce settlements are no more effective in reducing the probability of conflict than mediators who can only make non-binding recommendations. |
| Keywords: | Mediation, War and peace, Imperfect information, Communication games, Optimal mechanism |
| JEL: | C7 |
| Date: | 2010–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1765&r=gth |
| By: | Reddy, P.V.; Engwerda, J.C. (Tilburg University, Center for Economic Research) |
| Abstract: | In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an N player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto candidates as solving N constrained optimal control subproblems. We derive some weak conditions which entail one to find all Pareto candidates by solving a weighted sum optimal control problem. We observe that these conditions are related to transversality conditions of the associated subproblems. Furthermore, we derive sufficient conditions under which candidate Pareto solutions are indeed obtained by solving a weighted sum optimal control problem. We consider games defined by nonautonomous and discounted autonomous systems. The obtained results are used to analyze the regular indefinite linear quadratic infinite horizon differential game. For the scalar case we devise an algorithm to find all the Pareto optimal solutions. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:201056&r=gth |
| By: | Serra Garcia, M.; Damme, E.E.C. van; Potters, J.J.M. (Tilburg University, Center for Economic Research) |
| Abstract: | When truth conflicts with efficiency, can verbal communication destroy efficiency? Or are lies or vagueness used to hide inconvenient truths? We consider a sequential 2-player public good game in which the leader has private information about the value of the public good. This value can be low, high, or intermediate, with the latter case giving rise to a prisoners’ dilemma. Without verbal communication, efficiency is achieved, with contributions for high or intermediate values. When verbal com- munication is added, the leader has an incentive to hide the precise truth when the value is intermediate. We show experimentally that, when communication about the value must be precise, the leader frequently lies, preserving efficiency by exaggerating. When communication can be vague, the leader turns to vague messages when the value is intermediate, but not when it is high. Thus, she implicitly reveals all values. Inter- estingly, efficiency is still preserved, since the follower ignores messages altogether and does not seem to realize that vague messages hide inconvenient truths. |
| Keywords: | Communication;Efficiency;Lying;Public Goods. |
| JEL: | C72 C92 D83 H41 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:201080&r=gth |
| By: | Arroyo, Santiago; Alegría, Alexander |
| Abstract: | During the last 10 years, diplomatic relation between Colombia and Venezuela has been marked by a constant instability. Such a relation has had two hard moments: between December 2004 and February 2005 with Granda case, and in March 2008 with the dead of Raul Reyes. This paper shows an alternative analysis of agreements between both nations, emphasizing particularly the Granda case. The analysis is based on a dynamic game, through which it will be very important the effect on the economy of each country has the freezing of trade relation. |
| Keywords: | Teoría de juegos - intervención pública - implicaciones diplomáticas - acuerdos bilaterales. |
| JEL: | H70 C72 |
| Date: | 2009–09–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:24396&r=gth |
| By: | Michael A. Shields; Stephen Wheatley Price |
| Abstract: | In this paper they study bilateral bargaining problems with interested third parties, the stakeholders that enjoy benefits upon a bilateral agreement. We explore the strategic implications of this third party involvement. The main finding is that the potential willingness of the stakeholder to make contributions to promote agreement may be the source of severe inefficiency. However, and more surprisingly, for a wide range of parameter values this outcome is better for the stakeholder than if he enters bargaining directly. The results lend support to the tendency towards decentralisation of pay bargaining in the public sector in Europe.[IZA DP No. 395] |
| Keywords: | Bargaining, public sector, stakeholders, strikes, labour relations |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:ess:wpaper:id:2753&r=gth |
| By: | Israel Waichman; Artem Korzhenevych; Till Requate |
| Abstract: | In this paper we make use of a unique dataset collected in the central train station of Kiel, Germany. A group ticket is used by individual proposers who search for co-travelers to share the ride with shortly before the train departure. The bargaining behavior resembles the Ultimatum game to the extent that proposers request a fixed price for a shared ride and potential co-travelers usually accept or reject the deal. We observe that the prevailing price corresponds to the equal split of the ticket cost between the maximum possible number of co-travelers. This result is remarkable because the positions of the bargaining parties are hardly symmetric and the formation of the full group is not guaranteed. Using a simple agent-based model we are able to identify some sufficient conditions leading to the observed distribution of prices. Finally, we show that the probability to accept an unusually high offer is decreasing with the price and increasing when the offer is made right before the train departure |
| Keywords: | natural field experiment; bargaining; focal point; equal split; agent-based model |
| JEL: | C78 C93 D74 D83 |
| Date: | 2010–07 |
| URL: | http://d.repec.org/n?u=RePEc:kie:kieliw:1638&r=gth |
| By: | Hitoshi Matsushima (Faculty of Economics, University of Tokyo) |
| Abstract: | We model the stock market as a timing game, in which arbitrageurs who are not expected to be certainly rational compete over profit by bursting the bubble caused by investors’ euphoria. The manager raises money by issuing shares and the arbitrageurs use leverage. If leverage is weakly regulated, it is the unique Nash equilibrium that the bubble persists for a long time. This holds even if the euphoria is negligible and all arbitrageurs are expected to be almost certainly rational. This bubble causes serious harm to the society, because the manager uses the money raised for his personal benefit. |
| Keywords: | Euphoria, Leverage, Rational and Behavioral Arbitrageurs, Harmful Bubble, Unique Nash Equilibrium |
| JEL: | C72 C73 D82 G14 |
| Date: | 2010–08 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:711&r=gth |
| By: | Seamus Hogan (University of Canterbury); Hamish Kidd; Laura Meriluoto (University of Canterbury); Andrew Smith |
| Abstract: | The Fixed Price Offer (FPO) mechanism in Trade Me auctions allows sellers to make a take-it-or-leave-it offer at the conclusion of an unsuccessful auction. We investigate the effects of the FPO option on strategies and outcomes in independent-value auctions. The FPO option induces some bidders with a value above the seller’s reserve to wait for an FPO instead of bidding. Overall, the FPO option increases the probability of sale but reduces expected seller revenue compared to a standard auction. The impact of the FPO option is reduced when the number of bidders increases. |
| Keywords: | fixed price offer; private value auction; on-line auction; optimal reserve price; second chance offer |
| JEL: | D44 |
| Date: | 2010–08–13 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/51&r=gth |
| By: | Kocher, Martin G.; Pahlke, Julius; Trautmann, Stefan T. |
| Abstract: | Auctions often involve goods exhibiting a common knowledge ex-post risk that is independent of buyers’ private values or their signals regarding common value components. Esö and White (2004) showed theoretically that ex-post risk leads to precautionary bidding for DARA bidders: Agents reduce their bids by more than their appropriate risk premium. Testing precautionary bidding with data from the field seems almost impossible. We conduct experimental first-price auctions that allow us to directly identify the precautionary premium and find clear evidence for precautionary bidding. Bidders are significantly better off when a risky object rather than an equally valued sure object is auctioned. Our results are robust if we control for potentially confounding decision biases. |
| Keywords: | precautionary bidding; prudence; auction; experiment |
| JEL: | C91 D44 D81 |
| Date: | 2010–08 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:11743&r=gth |
| By: | Athanassoglou, Stergios; Sethuraman, Jay |
| Abstract: | This paper studies a generalization of the well known house allocation problem in which agents may own fractions of different houses summing to an arbitrary quantity, but have use for only the equivalent of one unit of a house. It departs from the classical model by assuming that arbitrary quantities of each house may be available to the market. Justified envy considerations arise when two agents have the same initial endowment, or when an agent is in some sense disproportionately rewarded in comparison to her peers. For this general model, an algorithm is designed to find a fractional allocation of houses to agents that satisfies ordinal efficiency, individual rationality, and no justified envy. The analysis extend to the full preference domain. Individual rationality, ordinal efficiency, and no justified envy conflict with weak strategyproofness. Moreover, individual rationality, ordinal efficiency and strategyproofness are shown to be incompatible. Finally, two reasonable notions of envy-freeness, no justified envy and equal-endowment no envy, conflict in the presence of ordinal efficiency and individual rationality. All of the impossibility results hold in the strict preference domain. |
| Keywords: | house allocation; fractional endowments; fairness; individual rationality |
| JEL: | C78 D71 C72 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:24351&r=gth |
| By: | Alex Dickson (Department of Economics, Strathclyde University) |
| Abstract: | We consider entry of additional firms into the market for a single commodity in which both sellers and buyers are permitted to interact strategically. We show that the market is quasi-competitive, in that the inclusion of an additional sellerlowers the price and increases the volume of trade, as expected. However, whilst buyers benefit from this change under reasonable conditions on preferences, we cannot conclude that sellers are always made worse off in the face of more intense competition, contrary to the conventional wisdom. We characterize the conditions under which entry by new sellers may raise the equilibrium profit of existing sellers, which will depend in an intuitive way on the elasticity of a strategic analog of demand and the market share of existing sellers, and encompass completely standard economic environments. |
| Keywords: | bilateral oligopoly; entry; comparative statics. |
| JEL: | C72 D21 D43 L13 |
| Date: | 2010–07 |
| URL: | http://d.repec.org/n?u=RePEc:str:wpaper:1011&r=gth |