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on Game Theory |
| By: | Flesch János; Perea Andrés (METEOR) |
| Abstract: | We consider discounted repeated games in which players can voluntarily purchase information about the opponents’ actions at past stages. Information about a stage can be bought at a fixed but arbitrary cost. Opponents cannot observe the information purchase by a player. For our main result, we make the usual assumption that the dimension of the set FIR of feasible and individually rational payoff vectors is equal to the number of players. We show that, if there are at least three players and each player has at least four actions, then every payoff vector in the interior of the set FIR can be achieved by a Nash equilibrium of the discounted repeated game if the discount factor is sufficiently close to 1. Therefore, nearly efficient payoffs can be achieved even if the cost of monitoring is high. We show that the same result holds if there are at least four players and at least three actions for each player. Finally, we indicate how the construction can be extended to sequential equilibrium. |
| Keywords: | mathematical economics; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007057&r=gth |
| By: | Caprari, E.; Tijs, S.H.; Torre, A. (Tilburg University, Center for Economic Research) |
| Abstract: | Inspired by Kalai-Samet [4] and Tijs [11], weighted average lexicographic values are introduced for share sets and for cores of cooperative games using induction arguments. Continuity properties and monotonicity properties of these weighted lexicographic values are studied. For subclasses of games (convex games, simplex games, big boss games) relations are established with weighted (exact) Shapley values. |
| Keywords: | Cooperative games;average lexicographic value;weighted Shapley value. |
| JEL: | C71 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:20088&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-theoretic 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 (i) the priors assign similar probabilities to all events that involve a player and his neighbors, and (ii) with high probability, a player believes, given his type, that his neighbors? conditional beliefs are close under the two priors, and that his neighbors believe, given their type, that. . . the conditional beliefs of their neighbors are close, for any number of iterations. |
| Keywords: | Network games;incomplete information;higher order beliefs;continuity;random networks;population uncertainty. |
| JEL: | C72 D82 L14 Z13 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:20085&r=gth |
| By: | Slikker, M.; Norde, H.W. (Tilburg University, Center for Economic Research) |
| Abstract: | The analysis of single-valued solution concepts for coalitional games with transferable utilities has a long tradition. Opposed to most of this literature we will not deal with solution concepts that provide payoffs to the players for the grand coalition only, but we will analyze allocation scheme rules, which assign payoffs to all players in all coalitions. We introduce four closely related allocation scheme rules for coalitional games. Each of these rules results in a population monotonic allocation scheme (PMAS) whenever the underlying coalitional game allows for a PMAS. The driving force behind these rules are monotonicities, which measure the payoff difference for a player between two nested coalitions. From a functional point of view these monotonicities can best be compared with the excesses in the definition of the (pre-)nucleolus. Two different domains and two different collections of monotonicities result in four allocation scheme rules. For each of the rules we deal with nonemptiness, uniqueness, and continuity, followed by an analysis of conditions for (some of) the rules to coincide. We then focus on characterizing the rules in terms of subbalanced weights. Finally, we deal with computational issues by providing a sequence of linear programs. |
| Keywords: | cooperative game theory;population monotonic allocation schemes;allocation scheme rules |
| JEL: | C71 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200806&r=gth |
| By: | Andrea Galeotti; Sanjeev Goyal; Matthew O. Jackson; Fernando Vega-Redondo; Leeat Yariv |
| Abstract: | In a variety of contexts - ranging from public goods provision to information collection - a player's well-being depends on own action as well as on the actions taken by his or her neighbors. We provide a framework to analyze such strategic interactions when neighborhood structure, modeled in terms of an underlying network of connections, a¤ects payo¤s. We provide results characterizing how the network structure, an individual.s position within the network, the nature of games (strategic substitutes versus complements and positive versus negative externalities), and the level of information, shape individual behavior and payoffs. |
| Keywords: | Networks, Network Games, Graphical Games, Diffusion, Incomplete Information |
| JEL: | D85 C72 L14 Z13 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2008/07&r=gth |
| By: | Alparslan-Gok, S.Z.; Miquel, S.; Tijs, S.H. (Tilburg University, Center for Economic Research) |
| Abstract: | Classification: JEL code C71 |
| Keywords: | Cooperative game theory;Interval uncertainty;Core;Value;Balancedness |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200809&r=gth |
| By: | Carlo Carraro (Department of Economics, University Of Venice Cà Foscari, Fondazione Eni Enrico Mattei, CEPR, CEPS and CMCC); Alessandra Sgobbi (Fondazione Eni Enrico Mattei and CMCC) |
| Abstract: | The objective of this paper is to investigate the usefulness of non-cooperative bargaining theory for the analysis of negotiations on water allocation and management. We explore the impacts of different economic incentives, a stochastic environment and varying individual preferences on players’ strategies and equilibrium outcomes through numerical simulations of a multilateral, multiple issues, non-cooperative bargaining model of water allocation in the Piave River Basin, in the North East of Italy. Players negotiate in an alternating-offer manner over the sharing of water resources (quantity and quality). Exogenous uncertainty over the size of the negotiated amount of water is introduced to capture the fact that water availability is not known with certainty to negotiating players. We construct the players’ objective function with their direct input. We then test the applicability of our multiple players, multi-issues, stochastic framework to a specific water allocation problem and conduct comparative static analyses to assess sources of bargaining power. Finally, we explore the implications of different attitudes and beliefs over water availability. |
| Keywords: | Bargaining, non-cooperative game theory, simulation models, uncertainty |
| JEL: | C61 C71 C78 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:28_07&r=gth |
| By: | Alejandro Saporiti (Economics, University of Manchester) |
| Abstract: | This paper analyzes the traditional unidimensional, two-party electoral competition game when parties have mixed motivations, in the sense that they are interested in winning the election, but also in the policy implemented after the contest. In spite of having discontinuous payoffs, this game, refer to as the hybrid election game, is shown to be payoff secure and reciprocally upper semi-continuous. Conditional payoffs, however, are not quasi-concave. Hence, the existence of a pure strategy Nash equilibrium (PSNE) is ensured only if parties have homogenous interests in power. In that case, an equilibrium not only exists, but it is also unique. Instead, if parties have heterogeneous motivations, depending upon the relationship between the electoral uncertainty, the aggregate opportunism and its distribution across parties, a psne may or may not exist. The mixed extension, however, is always better reply secure. Therefore, a mixed strategy Nash equilibrium do indeed exist. These results generalize previous existence results in unidimensional electoral competition. |
| Keywords: | Electoral competition; mixed motivations; discontinuous games; Nash equilibrium. |
| JEL: | C72 D72 D78 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:roc:wallis:wp50&r=gth |
| By: | Saran Rene (METEOR) |
| Abstract: | Previous literature proved the existence of an upper bound on the probability of trade in a bilateral trading problem when the valuations are distributed uniformly on [0,1]. This upper bound is achieved in the ½-double auction when the players play the Chatterjee-Samuelson strategies. We introduce behavioral-type players in a ½-double auction preceded by cheap talk. The behavioral-type players always declare a keenness to trade in the cheap-talk stage and play the Chatterjee-Samuelson strategies if they hear the “Keen” message. In equilibrium, the probability of trade between the strategic types increases monotonically as the probability of the behavioral types increases. If the probability of the behavioral types is high enough, the probability of trade between the strategic types is greater than the upper bound. |
| Keywords: | microeconomics ; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007048&r=gth |
| By: | Laslier, Jean-François (École Polytechnique); Weibull, Jörgen (Dept. of Economics, Stockholm School of Economics) |
| Abstract: | We consider a committee facing a binary decision under uncertainty. Each member holds some private information. Members may have different preferences and initial beliefs, but they all agree which decision should be taken in each of the two states of the world. We characterize the optimal anonymous and deterministic voting rule and provide a homogeneity assumption on preferences and beliefs under which sincere voting is a Nash equilibrium for this rule. We also provide a necessary and sufficient condition for sincere voting to be an equilibrium under any deterministic majoritarian voting rule. We show that a class of slightly randomized majoritarian voting rules make sincere voting a strict and unique pure-strategy equilibrium. A slight deontological preference for sincere voting, or ex post revelation of individual votes – ”transparency” – combined with a concern for esteem, has the same effect. |
| Keywords: | voting; condorcet; committee; jury; judgement aggregation. |
| JEL: | D71 D72 |
| Date: | 2008–01–28 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastef:0692&r=gth |
| By: | Saran Rene (METEOR) |
| Abstract: | We introduce trustworthy traders in bilateral trading. Trustworthy traders do not misrepresent their private information. We prove that an increase in the levels of trust (probabilities that traders are trustworthy) can reduce the maximum attainable probability of trade among the strategic traders in the set of k-double auctions. In contrast, if the levels of trust increase, then we can construct direct mechanisms with a higher probability of trade among the strategic traders. In fact, there exist ex-post efficient direct mechanisms if the levels of trust are high but k-double auctions are inefficient for all levels of trust. We prove that k-double auctions are constraint-inefficient for generic levels of trust when players have uniform priors. |
| Keywords: | microeconomics ; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007049&r=gth |
| By: | Daniela Di Cagno; Emanuela Sciubba (School of Economics, Mathematics & Statistics, Birkbeck) |
| Abstract: | We run a laboratory experiment were friendship networks are generated endogenously within an anonymous group. Our experiment builds on two phases in sequence: a network formation game and a trust game. We ?find that in those sessions where the trust game is played before the network formation game, the overall level of trust is not signi?cantly different from the one observed in a simple trust game; in those sessions where the trust game is played after the network formation game we ?find that the overall level of trust is signi?cantly lower than in the simple trust game. Hence surprisingly trust does not increase because of enforced reciprocity and moreover a common social history does affect the level of trust, but in a negative manner. Where network effects matter is in the choice of whom to trust: while we tend to trust less on average those with whom we have already interacted compared to total strangers, past history allows us to select whom to trust relatively more than others. |
| Keywords: | network formation, trust game, experiments |
| JEL: | C91 C92 L14 |
| Date: | 2008–01 |
| URL: | http://d.repec.org/n?u=RePEc:bbk:bbkefp:0801&r=gth |
| By: | Leufkens Kasper; Peeters Ronald; Vorsatz Marc (METEOR) |
| Abstract: | The presence of synergies in recurrent procurement auctions leads to an exposure problem and asymmetries among bidders. We consider sequential first- and second-price auctions with synergies in a setting with four bidders. In a series of experiments we compare the performance of the two pricing formats for three different sizes of the synergy. We find that for small synergies, the first-price auction performs better in terms of efficiency, revenue, and the probability on losses. However, once the synergy factor becomes very large the performance of the two different pricing formats becomes more similar. We also find that even though the potential total surplus that can be divided between buyers and seller increases in the synergy factor, subjects’ earnings within a pricing rule do not significantly change in the synergy factor. Finally, we observe that the two pricing formats give rise to different price trends within the auction sequence. In general, our results provide support for the common use of first-price instead of second-price auctions for public procurement. |
| Keywords: | industrial organization ; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007055&r=gth |
| By: | Morone, Andrea; Fiore, Annamaria; Sandri, Serena |
| Abstract: | A theory is said to be fully absorbable whenever its own acceptance by all of the individuals belonging to a certain population does not question its predictive validity. This accounts for strategic equilibria and can be related to the logic underlying convergence of behaviour and intentional herding in sequential games. This paper discusses the absorbability of informational cascades’ theory by bounded rational decision-makers and analyses whether providing individuals with theoretic information on informational cascades affects overall probability of herding phenomena to occur as well as whether an incorrect cascade can be reversed because of bounded rational adapting of the theory’s prescriptive. |
| Keywords: | Theory absorption; Herd behaviour; Informational cascades |
| JEL: | D8 C91 C72 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:6874&r=gth |
| By: | Klaus Bettina (METEOR) |
| Abstract: | We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. We investigate two new properties that capture the effect a newcomer has on incumbent agents. Competition sensitivity focuses on the newcomer as additional consumer and requires that some incumbents will suffer if competition is caused by a newcomer. Resource sensitivity focuses on the newcomer as additional resource and requires that this is beneficial for some incumbents. For solvable roommate markets, we provide the first characterizations of the core using either competition or resource sensitivity. On the class of all roommate markets, we obtain two associated impossibility results. |
| Keywords: | microeconomics ; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007046&r=gth |
| By: | Flesch János; Karagozoglu Emin; Perea Andrés (METEOR) |
| Abstract: | We investigate the problem in which an agent has to find an object that moves between two locations according to a discrete Markov process (see Pollock, 1970). At every period, the agent has three options: searching left, searching right, and waiting. We assume that waiting is costless whereas searching is costly. Waiting can be useful because it could induce a more favorable probability distribution over the two locations next period. We find an essentially unique (nearly) optimal strategy, and prove that it is characterized by two thresholds (as conjectured by Weber, 1986). We show, moreover, that it can never be optimal to search the location with the lower probability of containing the object. The latter result is far from obvious and is in clear contrast with the example in Ross (1983) for the model without waiting.We also analyze the case of multiple agents. This makes the problem a more strategic one, since now the agents not only compete against time but also against each other in finding the object. We find different kinds of subgame perfect equilibria, possibly containing strategies that are not optimal in the one agent case. We compare the various equilibria in terms of cost-effectiveness. |
| Keywords: | Strategy; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007051&r=gth |
| By: | George Ehrhardt; Matteo Marsili; Fernando Vega-Redondo |
| Abstract: | The paper proposes a model to study the conditions under which complex networks emerge (or not) when agents are involved in a dynamic coordination setup. The focus, however, is not on the classical issue of equilibrium selection - instead, our aim is to shed light on how agents' efforts to coordinate a¤ect the process of network formation in a large and complex environment. The model posits that, over time, new links are created if they are pro.table, and existing links disappear due to exogenous decay. Alongside this struggle between link creation and link destruction, agents' choices in the coordination game adapt to their current local conditions and thus coevolve with the social network. The dynamic behavior of the system is studied within di¤erent time scales (the long and ultralong runs), which di¤er in the role accorded to the noise that is induced by finite populations. We characterize analytically the evolution of the modelin each case and show that, depending on the time scale under consideration, the process displays discontinuous transitions in overall connectivity, resilient transformations in network topology, and equilibrium multiplicity. This behavior is akin to that observed concerning various network phenomena where coordination and network formation display mutually reinforcing roles. |
| JEL: | C73 D83 D85 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2008/08&r=gth |