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on Game Theory |
| By: | Teng , Jimmy |
| Abstract: | Bayesian rational prior equilibrium requires agent to make rational statistical predictions and decisions, starting with first order non informative prior and keeps updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. The main difference between the Bayesian theory of games and the current games theory are: I. It analyzes a larger set of games, including noisy games, games with unstable equilibrium and games with double or multiple sided incomplete information games which are not analyzed or hardly analyzed under the current games theory. II. For the set of games analyzed by the current games theory, it generates far fewer equilibria and normally generates only a unique equilibrium and therefore functions as an equilibrium selection and deletion criterion and, selects the most common sensible and statistically sound equilibrium among equilibria and eliminates insensible and statistically unsound equilibria. III. It differentiates between simultaneous move and imperfect information. The Bayesian theory of games treats sequential move with imperfect information as a special case of sequential move with observational noise term. When the variance of the noise term approaches its maximum such that the observation contains no informational value, there is imperfect information (with sequential move). IV. It treats games with complete and perfect information as special cases of games with incomplete information and noisy observation whereby the variance of the prior distribution function on type and the variance of the observation noise term tend to zero. Consequently, there is the issue of indeterminacy in statistical inference and decision making in these games as the equilibrium solution depends on which variances tends to zero first. It therefore identifies equilibriums in these games that have so far eluded the classical theory of games. |
| Keywords: | Games Theory; Bayesian Statistical Decision Theory; Prior Distribution Function; Conjectures; Subjective Probabilities |
| JEL: | C02 C11 C72 |
| Date: | 2010–07–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:24189&r=gth |
| By: | David J Butler (UWA Business School, The University of Western Australia); Victoria K Burbank (School of Social and Cultural Studies, The University of Western Australia); James S Chisholm (School of Anatomy and Human Biology, The University of Western Australia) |
| Abstract: | The tension between cooperative and competitive impulses is an eternal issue for every society. But how is this problem perceived by individual participants in the context of a behavioral games experiment? We first assess individual differences in players’ propensity to cooperate in a series of experimental games. We then use openended interviews with a subset of those players to investigate the various concepts (or ‘frames’) they used when thinking about self-interested and cooperative actions. More generally, we hope to raise awareness of player’s perceptions of experimental environments to inform both the design and interpretation of experiments and experimental data. |
| Keywords: | Laboratory Experiment, Frames, Selfishness, Cooperation |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:uwa:wpaper:10-03&r=gth |
| By: | Omer Biran (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX) |
| Abstract: | We study a first price auction preceded by a negotiation stage, during which bidders may form a bidding ring. We prove that in the absence of external effects the all-inclusive ring forms in equilibrium, allowing ring members to gain the auctioned object for a minimal price. However, identity dependent externalities may lead to the formation of small rings, as often observed in practice. Potential ring members may condition their participation on high transfer payments, as a compensation for their expected (negative) externalities if the ring forms. The others may therefore profitably exclude such "demanding" bidders, although risking tougher competition in the auction. We also analyze ring inefficiency in the presence of externalities, showing that a ring may prefer sending an inefficient member to the auction, if the efficient member exerts threatening externalities on bidders outside the ring, which in turn leads to a higher winning price. |
| Keywords: | Auctions;collusion;externalities;bargaining;sub-game perfect Nash equilibrium |
| Date: | 2010–07–23 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00505477_v1&r=gth |
| By: | Kwiek, Maksymilian |
| Abstract: | This paper considers a multi-unit ascending auction with two players and common values. A large set of equilibria in this model is not robust to a small reputational perturbation. In particular, if there is a positive probability that there is a type who always demands many units, regardless of price, then the model has a unique equilibrium payoff profile. If this uncertainty is only on one side, then the player who is known to be normal lowers her demand in order to stop the auction immediately at the reserve price. Hence, her possibly committed opponent buys all the units she demands at the lowest possible price. If the reputation is on both sides, then a War of Attrition emerges. <br><br> Keywords; Multi-unit auction, uniform price, ascending auction, reputation, aggressive bidding <br><br> JEL Classification: D44 |
| Date: | 2010–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:stn:sotoec:1012&r=gth |
| By: | Friederike Mengel (Universidad de Alicante); Gergely Horváth (Dpto. Fundamentos del Análisis Económico); Jaromir Kovarik (Universidad de Alicante) |
| Abstract: | We study a dynamic process where agents in a network interact in a Prisoner’s Dilemma. The network not only mediates interactions, but also information: agents learn from their own experience and that of their neighbors in the network about the past behavior of others. Each agent can only memorize the last h periods. Evolution selects among three preference types: altruists, defectors and conditional cooperators. We show - relying on simulation techniques - that the probability of reaching a cooperative state does not relate monotonically to the size of memory h. In fact it turns out to be optimal from a population viewpoint that there is a finite bound on agents’ memory capacities. We also show that it is the interplay of local interactions, direct and indirect reputation and memory constraints that is crucial for the emergence of cooperation. Taken by itself, none of these mechanisms is sufficient to yield cooperation. |
| Keywords: | evolution, reputation, bounded memory, cooperation. |
| JEL: | C70 C72 C73 |
| Date: | 2010–07 |
| URL: | http://d.repec.org/n?u=RePEc:ivi:wpasad:2010-25&r=gth |
| By: | Ianni, A.; Guarino, A. |
| Abstract: | We study a simple dynamic model of social learning with local informational exter-nalities. There is a large population of agents, who repeatedly have to choose one, out of two, reversible actions, each of which is optimal in one, out of two, unknown states of the world. Each agent chooses rationally, on the basis of private information (s)he receives by a symmetric binary signal on the state, as well as the observation of the action chosen among their nearest neighbours. Actions can be updated at revision opportunities that agents receive in a random sequential order. Strategies are stationary, in that they do not depend on time, nor on location. <br><br> We show that: if agents receive equally informative signals, and observe both neighbours, then the social learning process is not adequate and the process of actions converges exponentially fast to a configuration where some agents are permanently wrong; if agents are unequally informed, in that their signal is either fully informative or fully uninformative (both with positive probability), and observe one neighbour, then the social learning process is adequate and everybody will eventually choose the action that is correct given the state. Convergence, however, obtains very slowly, namely at rate ?t: We relate the findings with the literature on social learning and discuss the property of efficiency of the information transmission mechanism under local interaction. <br><br> Keywords; Social Learning, Bayesian Learning, Local Informational External-ities, Path Dependence, Consensus, Clustering, Convergence Rates. |
| Date: | 2010–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:stn:sotoec:1011&r=gth |
| By: | José Alcalde Pérez (Universidad de Alicante); José Angel Silva Reus (Universidad de Alicante); María del Carmen Marco Gil (Universidad Politécnica de Cartagena) |
| Abstract: | As it is known, there is no rule satisfying Additivity on the complete domain of bankruptcy problems. This paper proposes a notion of partial Additivity in this context, to be called µ-Additivity. We find that µ-Additivity, together with two quite compelling axioms, Anonymity and Continuity, identify the Minimal Overlap rule, introduced by O'Neill (1982). |
| Keywords: | bankruptcy problems, additivity, minimal overlap rule. |
| JEL: | C71 D63 D71 |
| Date: | 2010–07 |
| URL: | http://d.repec.org/n?u=RePEc:ivi:wpasad:2010-27&r=gth |
| By: | Marco Scarsini; Eilon Solan; Nicolas Vieille |
| Abstract: | We consider a class of auctions (Lowest Unique Bid Auctions) that have achieved a considerable success on the Internet. Bids are made in cents (of euro) and every bidder can bid as many numbers as she wants. The lowest unique bid wins the auction. Every bid has a fixed cost, and once a participant makes a bid, she gets to know whether her bid was unique and whether it was the lowest unique. Information is updated in real time, but every bidder sees only what's relevant to the bids she made. We show that the observed behavior in these auctions differs considerably from what theory would prescribe if all bidders were fully rational. We show that the seller makes money, which would not be the case with rational bidders, and some bidders win the auctions quite often. We describe a possible strategy for these bidders. |
| Date: | 2010–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1007.4264&r=gth |
| By: | Galbiati, Marco (Bank of England); Soramaki, Kimmo (Helsinki University of Technology) |
| Abstract: | This paper investigates the effect of liquidity-saving mechanisms (LSMs) in interbank payment systems. We model a stylised two-stream payment system where banks choose (a) how much liquidity to post and (b) which payments to route into each of two ‘streams’: the RTGS stream, and an LSM stream. Looking at equilibrium choices we find that, when liquidity is expensive, the two-stream system is more efficient than the vanilla RTGS system without an LSM. This is because the LSM achieves better co-ordination of payments, without introducing settlement risk. However, the two-stream system still only achieves a second-best in terms of efficiency: in many cases, a central planner could further decrease system-wide costs by imposing higher liquidity holdings, and without using the LSM at all. Hence, the appeal of the LSM resides in its ability to ease (but not completely solve) strategic inefficiencies stemming from externalities and free-riding. Second, ‘bad’ equilibria too are theoretically possible in the two-stream system. In these equilibria banks post large amounts of liquidity and at the same time overuse the LSM. The existence of such equilibria suggests that some co-ordination device may be needed to reap the full benefits of an LSM. In all cases, these results are valid for this particular model of an RTGS payment system and the particular LSM. |
| Keywords: | Payment system; RTGS; liquidity-saving mechanism |
| JEL: | C70 |
| Date: | 2010–07–29 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0400&r=gth |