|
on Game Theory |
| By: | Flam, Sjur (Economics Department, Bergen University); Ruszczynski, A. (Rutgers University, Department of Management Science and Information Systems) |
| Abstract: | This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or Nikaido-Isoda function is convex-concave, selected Nash equilibria correspond to diagonal saddle points of that function. This feature is exploited to design computational algorithms for finding such equilibria. To comply with some freedom of individual choice the algorithms developed here are fairly decentralized. However, since coupling constraints must be enforced, repeated coordination is needed while underway towards equilibrium. Particular instances include zero-sum, two-person games - or minimax problems - that are convex-concave and involve convex coupling constraints. |
| Keywords: | Noncooperative games; Nash equilibrium; joint constraints; quasivariational inequalities; exact penalty; subgradient projection; proximal point algorithm; partial regularization; saddle points; Ky Fan or Nikaido-Isoda functions |
| JEL: | C63 C70 |
| Date: | 2006–04–27 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2006_009&r=gth |
| By: | Takako Fujiwara-Greve (Department of Economics, Keio University; Department of Economics, Norwegian School of Management BI); Masahiro Okuno-Fujiwara (Faculty of Economics, University of Tokyo) |
| Abstract: | We develop a general framework to analyze endogenous relationships. To consider relationships in the modern society, neither one-shot games nor repeated games are appropriatemodelsbecausethe formationand dissolutionofa relationship is not an option. We formulate voluntarily separable repeated games, in which playersarerandomlymatchedtoplay acomponentgameaswellastochoose whether to play the game again with the same partner. There is no information ?ow across matches, and players areboundedly rational. We extend the notion of Neutrally Stable Distribution (NSD) to ?t for our model. When the component game is a prisoner's dilemma, NSD requires some trust-building periods to defect at the beginning of a partnership. We ?nd that polymorphic NSDs with voluntary breakups include strategies with shorter trust-building periods than any monomorphic NSD with no voluntary separation, and hence the average payo? ofpolymorphic NSD is higher. |
| Date: | 2006–04 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2006cf415&r=gth |
| By: | Branzei,Rodica; Fragnelli,Vito; Meca,Ana; Tijs,Stef (Tilburg University, Center for Economic Research) |
| Abstract: | We consider a market situation with two corners. One corner consists of a single seller with one object, and the other corner consists of potential buyers who all want the object. We suppose that the valuations of the object for the different buyers is known by all of them. Then two cooperative games, which we call the auction game and the ring game, corresponding to such a market situation are considered. Auction games are related to special total big boss games, while ring games are related to special convex games, the peer group games. It turns out that there exists a duality relation between the auction game and the ring game arising from the same two-corner market situation. For both classes of games relevant solution concepts are studied. |
| Keywords: | 91A12;90B05; market games;ring games;one-object auction situations;big boss games;peer group games |
| JEL: | C71 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200625&r=gth |
| By: | Carolyn Pitchik |
| Abstract: | I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder\\\'s type. Parameters permit the existence of multiple equilibrium symmetric bidding functions that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say α, is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good α is higher when good α is sold first. |
| Keywords: | sequential auctions, budget constraints, efficiency, revenue, price, sequence. |
| JEL: | C7 C72 L1 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-230&r=gth |
| By: | Kazuya Kamiya (Faculty of Economics, University of Tokyo); Takashi Shimizu (Department of Economics, Kansai University) |
| Abstract: | A conventional wisdom in economics is that a model dealing frictionless markets with a large number of agents always yields a Walrasian outcome. In this paper we assess the above argument in a dynamic framework by modeling centralized auction markets, and show that in such markets the outcomes are not necessarily Walrasian; the set of stationary equilibria in our model is a continuum which includes the Walrasian equilibrium. Moreover, we also buildamodelondecentralized auction markets and obtain similar results. |
| Date: | 2006–04 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2006cf417&r=gth |
| By: | Art Shneyerov |
| Date: | 2006–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:cla:uclatw:815595000000000009&r=gth |
| By: | Andrea Gallice (European University Institute) |
| Abstract: | We present a simple procedure that selects the strategies most likely to be played by inexperienced agents who interact in one shot 2x2 matching pennies games. As a first step we axiomatically describe players’ beliefs. We find the minimax regret criterion to be the simplest functional form that satisfies all the axioms. Then we hypothesize players act as if they were best responding to the belief their opponent plays accordino to minimax regret. When compared with existing experimental evidences about one shot matching pennies games, the procedure correctly indicates the choices of around 80% of the players. Applications to other classes of games are also explored. |
| Keywords: | Predictions, Minimax regret, Beliefs, Matching pennies, Experiments |
| JEL: | C72 C91 |
| Date: | 2006–02 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2006.31&r=gth |
| By: | Jurjen Kamphorst (Faculty of Law, Leiden University); Gerard van der Laan (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam) |
| Abstract: | We study how players in a local interaction hawk dove game will learn, if they can either imitate the most succesful player in the neighborhood or play a best reply versus the opponent's previous action. From simulations it appears that each learning strategy will be used, because each performs better when it is less popular. Despite that, clustering may occur if players choose their learning strategy on the basis of largely similar information. Finally, on average players will play Hawk with a probability larger than in the mixed Nash equilibrium of the stage game. |
| Keywords: | Learning; Local Interaction; Hawk-Dove game |
| JEL: | C73 |
| Date: | 2006–03–29 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20060034&r=gth |
| By: | Vives, Xavier (IESE Business School) |
| Abstract: | We provide sufficient conditions in finite-horizon multi-stage games for the value function of each player, associated to extremal Markov perfect equilibria, to display strategic complementarities and for the contemporaneous equilibrium to be increasing in the state variables. |
| Keywords: | Markov game; supermodularity; two-stage game; adjustment costs; learning curve; network effects; |
| Date: | 2006–03–21 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:iesewp:d-0619&r=gth |
| By: | Nielsen, Lars Relund (Biometry Research Unit); Pretolani, Daniele (Dipartimento de Matematica e Informatica); Andersen, Kim Allan (Department of Business Studies) |
| Abstract: | A substantial amount of research has been devoted to the shortest path problem in <p> networks where travel times are stochastic or (deterministic and) time-dependent. More <p> recently, a growing interest has been attracted by networks that are both stochastic and <p> time-dependent. In these networks, the best route choice is not necessarily a path, but <p> rather a time-adaptive strategy that assigns successors to nodes as a function of time. <p> In some particular cases, the shortest origin-destination path must nevertheless be chosen <p> a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a <p> priori shortest path is NP-hard, while the best time-adaptive strategy can be found in <p> polynomial time. <p> In this paper, we propose a solution method for the a priori shortest path problem, <p> and we show that it can be easily adapted to the ranking of the first K shortest paths. <p> Moreover, we present a computational comparison of time-adaptive and a priori route <p> choices, pointing out the effect of travel time and cost distributions. The reported results <p> show that, under realistic distributions, our solution methods are effective |
| Keywords: | Shortest paths; K shortest paths; stochastic time-dependent networks; routing; directed hypergraphs |
| Date: | 2004–11–18 |
| URL: | http://d.repec.org/n?u=RePEc:hhb:aaracc:92-006&r=gth |
| By: | R. Cellini; L. Lambertini |
| URL: | http://d.repec.org/n?u=RePEc:bol:bodewp:369&r=gth |
| By: | R. Cellini; L. Lambertini |
| URL: | http://d.repec.org/n?u=RePEc:bol:bodewp:402&r=gth |
| By: | Larry Karp (University of California, Berkeley and Giannini Foundation); Thierry Paul (IDEP/GREQAM) |
| Abstract: | In familiar models, a decrease in the friction facing mobile factors (e.g., lowering their adjustment costs) increases a coordination problem, leading to more circumstances where there are multiple equilibria. We show that a decrease in friction can decrease coordination problems if, for example, a production externality arises from a changing stock of knowledge or a changing environmental stock. In general, the relation between the amount of friction that mobile factors face and the likelihood of multiple equilibria is non-monotonic. |
| Keywords: | Indeterminacy, Multiple equilibria, Coordination games, Factor reallocation, Environmental externality, Learning-by-doing, Costs of adjustment, |
| Date: | 2005–02–08 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:agrebk:960r&r=gth |
| By: | Birgitte Sloth (Department of Business and Economics, University of Southern Denmark); Hans Jørgen Whitta-Jacobsen (Department of Economics, University of Copenhagen) |
| Abstract: | We define an evolutionary process of “economic Darwinism” for playing-the-field, symmetric games. The process captures two forces. One is “economic selection”: if current behavior leads to payoff differences, behavior yielding lowest payoff has strictly positive probability of being replaced by an arbitrary behavior. The other is “mutation”: any behavior has at any point in time a strictly positive, very small probability of shifting to an arbitrary behavior. We show that behavior observed frequently is in accordance with “evolutionary equilibrium”, a static equilibrium concept suggested in the literature. Using this result, we demonstrate that generally under positive (negative) externalities, economic Darwinism implies even more under- (over-) activity than does Nash equilibrium. |
| Keywords: | evolutionary game theory; Darwinian evolution; economic selection; mutation; evolutionary equilibrium; stochastic stability |
| JEL: | C72 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuieci:2006-01&r=gth |
| By: | L. Lambertini |
| URL: | http://d.repec.org/n?u=RePEc:bol:bodewp:370&r=gth |