Information Sharing and Cooperative Search in Fisheries

We present a dynamic game of search and learning about the productivity of com-peting fishing locations. Perfect Bayesian Nash equilibrium search patterns for non-cooperating fishermen and members of an information sharing cooperative are com-pared with first-best outcomes. Independent fishermen do not internalize the full valueof information, and do not replicate first-best search. A fishing cooperative faces afree-riding problem, as each coop member prefers that other members undertake costlysearch for information. Pooling contracts among coop members may mitigate, butare not likely to eliminate free riding. Our results explain the paucity of informationsharing in fisheries and suggest regulators use caution in advocating cooperatives as asolution to common pool ineffciencies in fisheries.�search; Information sharing; Dynamic Bayesian game; Fishing cooperative

Competitive Equilibria in Decentralized Matching with Incomplete Information

This paper shows that all perfect Bayesian equilibria of a dynamic matching game with two-sided incomplete information of independent private values variety are asymptotically Walrasian. Buyers purchase a bundle of heterogeneous, indivisible goods and sellers own one unit of an indivisible good. Buyer preferences and endowments as well as seller costs are private information. Agents engage in costly search and meet randomly. The terms of trade are determined through a Bayesian mechanism proposal game. The paper considers a market in steady state. As discounting and the fixed cost of search become small, all trade takes place at a Walrasian price. However, a robust example is presented where the limit price vector is a Walrasian price for an economy where only a strict subsets of the goods in the original economy are traded, i.e, markets are missing at the limit. Nevertheless, there exists a sequence of equilibria that converge to a Walrasian equilibria for the whole economy where all markets are open.Conditional CAPM

Pure Bayesian Nash equilibrium for Bayesian games with multidimensional vector Types and linear payoffs

We study $n$-agent Bayesian Games with $m$-dimensional vector types and linear payoffs, also called Linear Multidimensional Bayesian Games. This class of games is equivalent with $n$-agent, $m$-game Uniform Multigames. We distinguish between games that have a discrete type space and those with a continuous type space. More specifically, we are interested in the existence of pure Bayesian Nash Equilibrium for such games and efficient algorithms to find them. For continuous priors we suggest a methodology to perform Nash Equilibrium search in simple cases. For discrete priors we present algorithms that can handle two actions and two players games efficiently. We introduce the core concept of threshold strategy and, under some mild conditions, we show that these games have at least one pure Bayesian Nash Equilibrium. We illustrate our results with several examples like Double Game Prisoner Dilemna (DGPD), Chicken Game and Sustainable Adoption Decision Problem (SADP)

Competitive Equilibria in Decentralized Matching with Incomplete Information

This paper shows that all perfect Bayesian equilibria of a decentralized dynamic matching market with two-sided incomplete information of independent private values variety converge to competitive equilibria. Each buyer wants to purchase a bundle of heterogeneous, indivisible goods and each seller owns one unit of a heterogeneous indivisible good (as in Kelso and Crawford (1982) or Gul and Stacchetti (1999)). Buyer preferences and endowments as well as seller costs are private information. Agents engage in costly search and meet randomly. The terms of trade are determined through bilateral bargaining between buyers and sellers. The paper considers a market in steady state. It is shown that as frictions, i.e., discounting and fixed costs of search become small, all equilibria of the market game converge to perfectly competitive equilibria.Bargaining, Search, Matching

The Kalai-Smorodinski solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame

Interference Effects in Quantum Belief Networks

Probabilistic graphical models such as Bayesian Networks are one of the most powerful structures known by the Computer Science community for deriving probabilistic inferences. However, modern cognitive psychology has revealed that human decisions could not follow the rules of classical probability theory, because humans cannot process large amounts of data in order to make judgements. Consequently, the inferences performed are based on limited data coupled with several heuristics, leading to violations of the law of total probability. This means that probabilistic graphical models based on classical probability theory are too limited to fully simulate and explain various aspects of human decision making. Quantum probability theory was developed in order to accommodate the paradoxical findings that the classical theory could not explain. Recent findings in cognitive psychology revealed that quantum probability can fully describe human decisions in an elegant framework. Their findings suggest that, before taking a decision, human thoughts are seen as superposed waves that can interfere with each other, influencing the final decision. In this work, we propose a new Bayesian Network based on the psychological findings of cognitive scientists. We made experiments with two very well known Bayesian Networks from the literature. The results obtained revealed that the quantum like Bayesian Network can affect drastically the probabilistic inferences, specially when the levels of uncertainty of the network are very high (no pieces of evidence observed). When the levels of uncertainty are very low, then the proposed quantum like network collapses to its classical counterpart