Mistakes in cooperation: the stochastic stability of edgeworth's recontracting

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake-free) process consist of (i) all core allocations as absorbing states, and (ii) non-singleton classes of non-core allocations. Next, we introduce a perturbed process, where the resistance of each transition is a function of the number of agents that make mistakes -do not improve- in the transition and of the seriousness of each mistake. If preferences are always strict, we show that the unique stochastically stable state of the perturbed process is the Walrasian allocation. In economies with indifferences, non-core cycles are sometimes stochastically stable, while some core allocations are not. The robustness of these results is confirmed in a weak coalitional recontracting process

Game theory

game theory

Non-centralized Control for Flow-based Distribution Networks: A Game-theoretical Insight

This paper solves a data-driven control problem for a flow-based distribution network with two objectives: a resource allocation and a fair distribution of costs. These objectives represent both cooperation and competition directions. It is proposed a solution that combines either a centralized or distributed cooperative game approach using the Shapley value to determine a proper partitioning of the system and a fair communication cost distribution. On the other hand, a decentralized noncooperative game approach computing the Nash equilibrium is used to achieve the control objective of the resource allocation under a non-complete information topology. Furthermore, an invariant-set property is presented and the closed-loop system stability is analyzed for the non cooperative game approach. Another contribution regarding the cooperative game approach is an alternative way to compute the Shapley value for the proposed specific characteristic function. Unlike the classical cooperative-games approach, which has a limited application due to the combinatorial explosion issues, the alternative method allows calculating the Shapley value in polynomial time and hence can be applied to large-scale problems.Generalitat de Catalunya FI 2014Ministerio de Ciencia y Educación DPI2016-76493-C3-3-RMinisterio de Ciencia y Educación DPI2008-05818Proyecto europeo FP7-ICT DYMASO

Strongly Rational Sets for Normal-Form Games

Curb sets [Basu and Weibull, Econ. Letters 36 (1991), 141-146] are product sets of pure strategies containing all individual best-responses against beliefs restricted to the recommendations to the remaining players. The concept of minimal curb sets is a set-theoretic coarsening of the notion of strict Nash equilibrium. We introduce the concept of minimal strong curb sets which is a set-theoretic coarsening of the notion of strong Nash equilibrium. Strong curb sets are product sets of pure strategies such that each player.s set of recommended strategies must contain all coalitional best-responses of each coalition to whatever belief each coalition member may have that is consistent with the recommendations to the other players. Minimal strong curb sets are shown to exist and are compared with other well known solution concepts. We also provide a dynamic learning process leading the players to playing strategies from a minimal strong curb set.mathematical economics;

Game-theoretic Resource Allocation Methods for Device-to-Device (D2D) Communication

Device-to-device (D2D) communication underlaying cellular networks allows mobile devices such as smartphones and tablets to use the licensed spectrum allocated to cellular services for direct peer-to-peer transmission. D2D communication can use either one-hop transmission (i.e., in D2D direct communication) or multi-hop cluster-based transmission (i.e., in D2D local area networks). The D2D devices can compete or cooperate with each other to reuse the radio resources in D2D networks. Therefore, resource allocation and access for D2D communication can be treated as games. The theories behind these games provide a variety of mathematical tools to effectively model and analyze the individual or group behaviors of D2D users. In addition, game models can provide distributed solutions to the resource allocation problems for D2D communication. The aim of this article is to demonstrate the applications of game-theoretic models to study the radio resource allocation issues in D2D communication. The article also outlines several key open research directions.Comment: Accepted. IEEE Wireless Comms Mag. 201

MISTAKES IN COOPERATION: THE STOCHASTIC STABILITY OF EDGEWORTH'S RECONTRACTING

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake-free) process consist of (i) all core allocations as absorbing states, and (ii) non-singleton classes of non-core allocations. Next, we introduce a perturbed process, where the resistance of each transition is a function of the number of agents that make mistakes –do not improve– in the transition and of the seriousness of each mistake. If preferences are always strict, we show that the unique stochastically stable state of the perturbed process is the Walrasian allocation. In economies with indifferences, non-core cycles are sometimes stochastically stable, while some core allocations are not. The robustness of these results is confirmed in a weak coalitional recontracting process.

Mistakes in cooperation: the stochastic stability of edgeworth's recontracting.

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake-free) process consist of (i) all core allocations as absorbing states, and (ii) non-singleton classes of non-core allocations. Next, we introduce a perturbed process, where the resistance of each transition is a function of the number of agents that make mistakes -do not improve- in the transition and of the seriousness of each mistake. If preferences are always strict, we show that the unique stochastically stable state of the perturbed process is the Walrasian allocation. In economies with indifferences, non-core cycles are sometimes stochastically stable, while some core allocations are not. The robustness of these results is confirmed in a weak coalitional recontracting process.