|
on Game Theory |
| By: | René van den Brink (Vrije Universiteit Amsterdam); René Levinsky (Max Planck Institute of Economics, Jena, Germany); Miroslav Zeleny (Charles University, Prague, Czech Republic) |
| Abstract: | The Shapley value of a cooperative transferable utility game distributes the dividend of each coalition in the game equally among its members. Given exogenous weights for all players, the corresponding weighted Shapley value distributes the dividends proportionally to their weights. In this contribution we define the balanced solution which assigns weights to players such that the corresponding weighted Shapley value of each player is equal to her weight. We prove its existence for all monotone transferable utility games, discuss other properties of this solution, and deal with its characterization through a reduced game consistency. |
| Keywords: | Balanced solution; Proportionality; Reduced game consistency; Weighted Shapley value |
| JEL: | C71 |
| Date: | 2007–10–12 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20070073&r=gth |
| By: | Alparslan-Gok, S.Z.; Branzei, R.; Tijs, S.H. (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper, interval-type solution concepts for interval-valued cooperative games like the interval core, the interval dominance core and stable sets are introduced and studied. The notion of I-balancedness is introduced, and it is proved that the interval core of an interval-valued cooperative game is nonempty if and only if the game is I-balanced. Relations between the interval core, the dominance core and stable sets of an interval-valued game are established. |
| Keywords: | cooperative games;interval games;the core;the dominance core;stable sets |
| JEL: | C71 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200817&r=gth |
| By: | René van den Brink (VU University, Amsterdam); Yukihiko Funaki (Waseda University, Tokyo, Japan); Yuan Ju (Keele University, Keele, UK) |
| Abstract: | One of the main issues in economics is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide tools that make it possible to study this trade-off in a consistent way by providing three types of results on egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, we show that all these solutions satisfy the same reduced game consistency. Second, we characterize this class of solutions using monotonicity properties. Finally, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game. |
| Keywords: | Shapley value; Equal division solution; Egalitarian Shapley value; Reduced Game Consistency; Monotonicity; Implementation |
| JEL: | C71 C72 D60 |
| Date: | 2007–08–24 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20070062&r=gth |
| By: | Harold Houba (VU University Amsterdam); Quan Wen (Vanderbilt University, Nashville) |
| Abstract: | We study a bargaining model with a disagreement game between offers and counteroffers. In order to characterize the set of its subgame perfect equilibrium payoffs, we provide a recursive technique that relies on the Pareto frontier of equilibrium payoffs. When players have different time preferences, reaching an immediate agreement may not be Pareto efficient. The recursive technique developed in this paper generalizes that of Shaked and Sutton (1984) by incorporating the possibility of making unacceptable proposals into the backward induction analysis. Results from this paper extend all the previous findings and resolve some open issues in the current literature. |
| Keywords: | Bargaining; negotiation; time preference; endogenous threats |
| JEL: | C72 C73 C78 |
| Date: | 2007–09–12 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20070070&r=gth |
| By: | Said, Maher |
| Abstract: | We examine a model in which multiple buyers with single-unit demand are faced with an infinite sequence of auctions. New buyers arrive on the market probabilistically, and are each endowed with a constant private value. Moreover, objects also arrive on the market at random times, so the number of competitors and the degree of informational asymmetry among them may vary across from one auction to the next. We demonstrate by way of a simple example the inefficiency of the second-price sealed-bid auction in this setting, and therefore assume that each object is sold via ascending auction. We then characterize an efficient and fully revealing equilibrium for the game in which the objects are sold via ascending auctions. We show that each buyer's bids and payoffs depend only upon their rank amongst their competitors and the (revealed) values of those with lower values. Furthermore, strategies are memoryless---bids depend only upon the information revealed in the current auction, and not on any information that may have been revealed in earlier periods. We then demonstrate that the sequential ascending auction serves as an indirect mechanism that is equivalent---in our setting---to the dynamic marginal contribution mechanism introduced by Bergemann and Välimäki (2007) and generalized in Cavallo et al. (2007). |
| Keywords: | Sequential auctions; Ascending auctions; Random arrivals; Information revelation; Dynamic Vickrey-Clarke-Groves mechanism; Marginal contribution |
| JEL: | D44 D83 C73 |
| Date: | 2008–02–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:7160&r=gth |
| By: | Ettore Damiano; Hao Li; Wing Suen |
| Abstract: | We study a model of collective decision making in which agents vote on the decision repeatedly until they agree, with the agents receiving no exogenous new information between two voting rounds but incurring a delay cost. Although preference conflict between the agents makes information aggregation impossible in a single round of voting, in the equilibrium of the repeated voting game agents are increasingly more willing to vote their private information after each disagreement. Information is efficiently aggregated within a finite number of rounds. As delay becomes less costly, agents are less willing to vote their private information, and efficient information aggregation takes longer. Even as the delay cost converges to zero, agents are strictly better off in the repeated voting game than in any single round game for moderate degrees of initial conflict. |
| Keywords: | repeated voting; gradual concessions; small delay cost |
| JEL: | C78 D82 |
| Date: | 2008–02–14 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-311&r=gth |
| By: | John Duggan; Yoji Sekiya (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158) |
| Abstract: | We consider a general plurality voting game with multiple candidates, where voter preferences over candidates are exogenously given. In particular, we allow for arbitrary voter indierences, as may arise in voting subgames of citizen-candidate or locational models of elections. We prove that the voting game admits pure strategy equilibria in undominated strategies. The proof is constructive: we exhibit an algorithm, the “best winning deviation” algorithm, that produces such an equilibrium in finite time. A byproduct of the algorithm is a simple story for how voters might learn to coordinate on such an equilibrium. |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:roc:wallis:wp52&r=gth |
| By: | Kfir Eliaz; Ariel Rubinstein |
| Date: | 2008–02–18 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001909&r=gth |
| By: | Bourjade, Sylvain |
| Abstract: | Uniform price auctions admit a continuum of collusive seeming equilibria due to bidders' market power. In this paper, I modify the auction rules in allowing the seller to ration strategic bidders in order to ensure small bidders' participation. I show that many of these "bad" equilibria disappear when strategic bidders do not know small bidders' willingness to pay. Moreover, when the seller is unconstrained in the quantity she can allocate to small bidders, the unique equilibrium price is the highest that the seller could get. |
| Keywords: | Uniform price Auctions, Treasury Auctions, IPO, Rationing |
| JEL: | D44 G32 |
| Date: | 2003–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:7250&r=gth |
| By: | Dominic Rohner (University of York) |
| Abstract: | Social tensions impede social cohesion and public goods provision. They can also be a driving force for more serious conflicts such as civil wars. Surprisingly, however, the emergence of social tensions has only rarely been studied in the literature. In the present contribution a game-theoretic model highlights how reputation concerns and the structure of group cleavages matter for the emergence of social tensions. In particular, the respective effects of fractionalisation, polarisation and segregation are assessed. The predictions of the model can account for recent empirical evidence on ethnic conflicts. The framework can also be applied to the study of social capital and merger failures. |
| Keywords: | Conflict, Information, Reputation, Ethnicity, Social Capital |
| JEL: | C73 D74 L14 Z13 |
| Date: | 2008–01 |
| URL: | http://d.repec.org/n?u=RePEc:hic:wpaper:40&r=gth |
| By: | Alexander Stremitzer (University of Bonn, Wirtschaftspolitische Abteilung, Adenauerallee 24-42, 53113 Bonn, Germany; alexander.stremitzer@uni-bonn.de.) |
| Abstract: | We consider a model of a single defendant and N plaintiffs where the total cost of litigation is fixed on the part of the plaintiffs and shared among the members of a suing coalition. By settling and dropping out of the coalition, a plaintiff therefore creates a negative externality on the other plaintiffs. It was shown in Che and Spier (2007) that failure to internalize this externality can often be exploited by the defendant. However, if plaintiffs make sequential take-it-or-leave-it settlement offers, we can show that they will actually be exploited by one of their fellow plaintiffs rather than by the defendant. Moreover, if litigation is a public good as is the case in shareholder derivative suits, parties may fail to reach a settlement even having complete information. This may explain why we observe derivative suits in the US but not in Europe. |
| Keywords: | litigation, settlement, bargaining, contracting with externalities, derivative suits, public goods |
| JEL: | K41 C7 H4 |
| Date: | 2008–01 |
| URL: | http://d.repec.org/n?u=RePEc:trf:wpaper:224&r=gth |
| By: | Paul A. Grout; Sebastien Mitraille; Silvia Sonderegger |
| Abstract: | Much of the literature on diversity assumes that individuals have an exogenous "taste for discrimination". In contrast with this approach, we build a model where preferences over the nature of one's community are derived indirectly, and arise because the composition of the community determines the behavior of its members. This allows us to gain a far deeper understanding of the forces that underpin the desirability of diversity or homogeneity within communities. Our main contribution is to show that there are always counteracting forces (heterogeneity involves both costs and benefits), and that, although people prefer to live in communities where their type is majoritarian, they always benefit from having some heterogeneity in the composition of their community. |
| Keywords: | heterogeneity, social interactions, value of information, complementarities. |
| JEL: | C7 D82 Z1 |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:bri:cmpowp:07/191&r=gth |