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on Game Theory |
| By: | Kleppe, J.; Hendrickx, R.L.P.; Borm, P.E.M.; Garcia-Jurado, I.; Fiestras-Janeiro, G. (Tilburg University, Center for Economic Research) |
| Abstract: | This paper analyses the role of transfer payments and strategic con- tracting within two-person strategic form games with monetary pay- offs. First, it introduces the notion of transfer equilibrium as a strat- egy combination for which individual stability can be supported by allowing the possibility of transfers of the induced payoffs. Clearly, Nash equilibria are transfer equilibria, but under common regularity conditions the reverse is also true. This result typically does not hold for finite games without the possibility of randomisation, and transfer equilibria for this particular class are studied in some detail. The second part of the paper introduces, also within the setting of finite games, contracting on monetary transfers as an explicit strategic option, resulting in an associated two-stage contract game. In the first stage of the contract game each player has the option of proposing transfer schemes for an arbitrary collection of outcomes. Only if the players fully agree on the entire set of transfer proposals, the payoffs of the game to be played in the second stage are modified accordingly. The main results provide explicit characterisations of the sets of payoff vectors that are supported by Nash equilibrium and virtual subgame perfect equilibrium, respectively. |
| Keywords: | monetary transfer scheme;transfer equilibrium;contract game;virtual subgame perfect equilibrium;Folk theorems |
| JEL: | C72 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200724&r=gth |
| By: | Engwerda, J.C. (Tilburg University, Center for Economic Research) |
| Abstract: | In this note we present as well necessary as sufficient conditions for existence of a Pareto optimum for general non-convex differential games. The obtained results are used to analyze the non-convex regular indefinite linear quadratic differential game. For the scalar case an algorithm is devised to find all Pareto efficient solutions. |
| Keywords: | Dynamic Optimization;Pareto Efficiency;Cooperative Differential Games;LQ theory. |
| JEL: | C61 C71 C73 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200742&r=gth |
| By: | Branzei, R.; Llorca, N.; Sanchez-Soriano, J.; Tijs, S.H. (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper we introduce the equal division core for arbitrary multi-choice games and the constrained egalitarian solution for con- vex multi-choice games, using a multi-choice version of the Dutta-Ray algorithm for traditional convex games. These egalitarian solutions for multi-choice games have similar properties as their counterparts for traditional cooperative games. On the class of convex multi-choice games, we axiomatically characterize the constrained egalitarian solu- tion. |
| Keywords: | Multi-choice games;Convex games;Equal division core;Constrained egalitarian solution. |
| JEL: | C71 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200755&r=gth |
| By: | Branzei, R.; Tijs, S.H.; Zarzuelo, J. (Tilburg University, Center for Economic Research) |
| Abstract: | This paper focuses on new characterizations of convex multi-choice games using the notions of exactness and superadditivity. Further- more, (level-increase) monotonic allocation schemes (limas) on the class of convex multi-choice games are introduced and studied. It turns out that each element of the Weber set of such a game is ex- tendable to a limas, and the (total) Shapley value for multi-choice games generates a limas for each convex multi-choice game. |
| Keywords: | Multi-choice games;Convex games;Marginal games;Weber set;Monotonic allocation schemes. |
| JEL: | C71 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200754&r=gth |
| By: | Antonio Romero Medina; Mateo Triossi |
| Abstract: | The paper studies two games of capacity manipulation in hospital-intern markets. The focus is on the stability of Nash equilibrium outcomes. We provide minimal necessary and sufficient conditions guaranteeing the existence of pure strategy Nash Equilibria and the stability of outcomes. |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:we075933&r=gth |
| By: | Kets, W. (Tilburg University, Center for Economic Research) |
| Abstract: | Networks can have an important effect on economic outcomes. Given the complexity of many of these networks, agents will generally not know their structure. We study the sensitivity of game-theoretical predictions to the specification of players? (common) prior on the network in a setting where players play a fixed game with their neighbors and only have local information on the network structure. We show that two priors are close in a strategic sense if and only if (1) the priors assign similar probabilities to all events that involve a player and his neighbors, and (2) with high probability, a player believes, given his type, that his neighbors? conditional beliefs are similar, and that his neighbors believe, given their type, that. . . the conditional beliefs of their neighbors are similar, for any number of iterations. Also, we show that the common but unrealistic assumptions that the size of the network is common knowledge or that the types of players are independent are far from innocuous: if these assumptions are violated, small probability events can have a large effect on outcomes through players? conditional beliefs. |
| Keywords: | Network games;incomplete information;higher order beliefs;continuity;random networks;population uncertainty. |
| JEL: | C72 D82 L14 Z13 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200746&r=gth |
| By: | Lohman, E.; Borm, P.E.M.; Quant, M. (Tilburg University, Center for Economic Research) |
| Abstract: | This paper revisits the Alexia value, a recent solution concept for cooperative transferable utility games. We introduce the dual Alexia value and show that it coincides with the Alexia value for several classes of games. We demonstrate the importance of the notion of compromise stability for characterizing the Alexia value. |
| Keywords: | Alexia value;dual Alexia value;compromise stability;bankruptcy |
| JEL: | C71 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200752&r=gth |
| By: | Gerichhausen, M.; Hamers, H.J.M. (Tilburg University, Center for Economic Research) |
| Abstract: | The research that studies the interaction between sequencing situations and cooperative games, that started with the paper of Curiel et al. (1989), has become an established line of research. This paper introduces a new model in this field: partitioning sequencing situations and games. The characteristic of partitioning sequencing situations is that the jobs arrive in batches, and those jobs that arrive in earlier batches have some privileges over jobs in later arrived batches. For partitioning sequencing situations we introduce and characterise the partitioning equal gain splitting rule. Next, we define cooperative games that arise from these partitioning sequencing situations. It is shown that these games are convex. Moreover, we present a game independent expression for the Shapley value. Finally, it is shown that the partitioning equal gain splitting rule can be used to generate a core allocation and can be viewed as the average of two specific marginal vectors. |
| Keywords: | Sequencing situations;sequencing games. |
| JEL: | C71 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200740&r=gth |
| By: | Engwerda, J.C. (Tilburg University, Center for Economic Research) |
| Abstract: | We survey some recent research results in the field of dynamic cooperative differential games with non-transferable utilities. Problems which fit into this framework occur for instance if a person has more than one objective he likes to optimize or if several persons decide to combine efforts in trying to realize their individual goals. We assume that all persons act in a dynamic environment and that no side-payments take place. For these kind of problems the notion of Pareto efficiency plays a fundamental role. In economic terms, an allocation in which no one can be made better-off without someone else becoming worseoff is called Pareto efficient. In this paper we present as well necessary as sufficient conditions for existence of a Pareto optimum for general non-convex games. These results are elaborated for the special case that the environment can be modeled by a set of linear differential equations and the objectives can be modeled as functions containing just affine quadratic terms. Furthermore we will consider for these games the convex case. In general there exists a continuum of Pareto solutions and the question arises which of these solutions will be chosen by the participating persons. We will flash some ideas from the axiomatic theory of bargaining, which was initiated by Nash [16, 17], to predict the compromise the persons will reach. |
| Keywords: | Dynamic Optimization;Pareto Efficiency;Cooperative Differential Games;LQ The- ory;Riccati Equations;Bargaining |
| JEL: | C61 C71 C73 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200741&r=gth |
| By: | Andrea Galeotti; Sanjeev Goyal |
| Abstract: | The law of the few refers to the following empirical phenomenon: in social groups a very small subset of individuals invests in collecting information while the rest of the group invests in forming connections with this select few. In many instances, there are no observable differences in characteristics between those who invest in information and those who invest in forming connections. This paper shows that the law of few naturally emerges in environments with identical rational agents. We develop a strategic game in which players have the opportunity to invest in collecting information as well as in investing in bilateral connections with others. We find that every strict equilibrium of this game exhibits the ‘law of the few’. We also show that this pattern of social differentiations is efficient in some cases. |
| Date: | 2007–08–29 |
| URL: | http://d.repec.org/n?u=RePEc:esx:essedp:636&r=gth |
| By: | Flavio M. Menezes & Matthew J. Ryan (School of Economics, The University of Queensland) |
| Abstract: | We extend the Coase conjecture to the case of a seller with a single object, who faces n potential buyers and holds a sequence of English auctions until the object is sold. In an independent-private-values environment in which buyers and sellers share the same discount factor, we show that the (perfect Bayesian) equilibrium path of reserve prices obeys a Coasian logic. Moreover, the equilibrium reserve path lies below that for the model of repeated sealed-bid, second-price auctions studied by McAfee and Vincent (1997). Nevertheless, the open (English) and sealed-bid formats are shown to be revenue equivalent. |
| URL: | http://d.repec.org/n?u=RePEc:qld:uq2004:349&r=gth |
| By: | Talman, A.J.J.; Yang, Z.F. (Tilburg University, Center for Economic Research) |
| Abstract: | A number of heterogeneous items are to be sold to several bidders. Each bidder demands at most one item. The price of each item is not completely flexible and is restricted to some admissible interval. In such a market economy with price rigidities, a Walrasian equilibrium usually fails to exist. To facilitate the allocation of items to the bidders, we propose an ascending auction with rationing that yields a constrained Walrasian equilibrium outcome. The auctioneer starts with the lower bound price vector that specifies the lowest admissible price for each item, and each bidder responds with a set of items demanded at those prices. The auctioneer adjusts prices upwards for a minimal set of over-demanded items and chooses randomly a winning bidder for any item if the item is demanded by several bidders and its price has reached its highest admissible price. We prove that the auction finds a constrained Walrasian equilibrium outcome in a finite number of steps. |
| Keywords: | Ascending auction;multi-item auction;constrained equilibrium;price rigidities;rationing. |
| JEL: | D44 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200726&r=gth |
| By: | Gary E Bolton; Axel Ockenfels |
| Abstract: | In a seminal paper, Kreps and Wilson (1982) remark that, with regard to reputation building in the chain store game, it does not matter whether interaction is among long-term partners or one-shot strangers. We show that this remark is incorrect: in sequential equilibrium, the effectiveness of reputation building depends on the matching procedure. The reason is that the benefits of the information obtained by challenging the incumbent are internalized in the partners case but externalized in the strangers case. Perhaps surprisingly, the same intuition does not hold for the buyer-seller game with seller moral hazard; there, in sequential equilibrium, the way information disseminates in the market is irrelevant for the success of reputation building. An experiment finds that matching significantly affects reputation building behavior in both games although the size of the effect is more modest in the buyer-seller case. |
| Date: | 2007–08–04 |
| URL: | http://d.repec.org/n?u=RePEc:kls:series:0035&r=gth |
| By: | Juergen Huber (University of Innsbruck); Martin Shubik (Cowles Foundation, Yale University); Shyam Sunder (Yale University) |
| Abstract: | Is personal credit issued by participants sufficient to operate an economy efficiently, with no outside or government money? Sorin (1995) constructed a strategic market game to prove that this is possible. We conduct an experimental game in which each agent issues her own IOUs and a costless efficient clearinghouse adjusts the exchange rates among them so the markets always clear. The results suggest that if the information system and clearing are so good as to preclude moral hazard, any form of information asymmetry, or need for trust, the economy operates efficiently at any price level without government money. Conversely, perhaps explanations for prevalence of government money should be sought in either the above mentioned frictions or our unwillingness to experiment with innovation. |
| Keywords: | Government and individual money, Efficiency, Experimental gaming |
| JEL: | C73 C91 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1622&r=gth |
| By: | Pablo T Spiller; Rafael Gely |
| Date: | 2007–08–24 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:122247000000001409&r=gth |