
on Game Theory 
By:  Scalzo, Vincenzo 
Abstract:  We present a new concept for (generalized) strategic form games, called \emph{doubly strong equilibrium}, and give an existence result when the players have nonordered and discontinuous preferences. Since a doubly strong equilibrium is a strong equilibrium in the sense of Aumann, we get the existence of strong equilibria in discontinuous games. The result has been obtained by using the \emph{quasiKy Fan minimax inequality}. Applications to exchange economies are given. We prove the existence of \emph{doubly strong allocations}, which maximize consumers' preferences on the set of feasible allocations. The doubly strong allocations belong to the core of the economy. When consumers' preferences are selfish, we have that the doubly strong allocations are fair in the sense of Schmeidler and Yaari. So, we get the existence of fair allocations in the setting of nonordered and discontinuous preferences.\ 
Keywords:  Generalized games.Discontinuous and nonordered preferences. Doubly strong equilibrium. QuasiKy Fan minimax inequality. Exchange economies. Core allocations. Fair allocations. 
JEL:  C60 C70 D51 D63 
Date:  2020–03–28 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:99329&r=all 
By:  Itai Arieli (Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology); Yakov Babichenko (Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology); Ron Peretz (Department of Economics, Bar Ilan University); H. Peyton Young (London School of Economics and Nuffield College, University of Oxford) 
Abstract:  New ways of doing things often get started through the actions of a few innovators, then diffuse rapidly as more and more people come into contact with prior adopters in their social network. Much of the literature focuses on the speed of diffusion as a function of the network topology. In practice, however, the topology may not be known with any precision, and it is constantly in flux as links are formed and severed. Here we establish an upper bound on the expected waiting time until a given proportion of the population has adopted that holds independently of the network structure. Kreindler and Young [33, 2014] demonstrated such a bound for regular networks when agents choose between two options: the innovation and the status quo. Our bound holds for directed and undirected networks of arbitrary size and degree distribution, and for multiple competing innovations with different payoffs. 
Date:  2019–08–22 
URL:  http://d.repec.org/n?u=RePEc:nuf:econwp:1907&r=all 
By:  Ozdogan, Ayca; Saglam, Ismail 
Abstract:  In this paper, we extend Aumann's (1974) wellknown solution of correlated equilibrium to allow for a cost of disobedience for each player. Calling the new solution costly correlated equilibrium (CCE), we derive the necessary and sufficient conditions under which the set of CCE strictly expands when the players' cost of disobedience is increased by the mediator in any finite normalform game. These conditions imply that for any game that has a Nash equilibrium (NE) that is unpure, the set of CCE strictly expands with the addition of even arbitrarily small cost of disobedience, whereas for games that have a unique NE in pure strategies, the set of CCE stays the same unless the cost gets sufficiently high. We also study the welfare implications and changes in the value of mediation with exogenous cost changes. We find that strictly better social outcomes can be attained and the value of mediation cannot decrease with an increase in the cost level. We also illustrate how our model can be integrated with a costselection game where players noncooperatively choose their costs of disobedience before mediation occurs. We show that there exist costselection games in which setting the cost of disobedience at zero is a strictly dominated strategy for each player as well as games this strategy becomes weakly dominant for everyone. 
Keywords:  Correlated equilibrium; cost of disobedience. 
JEL:  C72 
Date:  2020–03–30 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:99370&r=all 
By:  Besner, Manfred 
Abstract:  Exponential runtimes of algorithms for TUvalues like the Shapley value are one of the biggest obstacles in the practical application of otherwise axiomatically convincing solution concepts of cooperative game theory. We discuss how the hierarchical structure of a level structure improves the runtimes compared to an unstructured set of players. As examples, we examine the Shapley levels value, the nested Shapley levels value, and, as a new LSvalue, the nested Owen levels value. Polynomialtime algorithms for these values (under ordinary conditions) are provided. Furthermore, we introduce relevant coalition functions where all coalitions which are not relevant for the payoff calculation have a Harsanyi dividend of zero. By these coalition functions, our results shed new light on the computation of values of the Harsanyi set and many values from extensions of this set. 
Keywords:  Cooperative game · Polynomialtime algorithm · Level structure · (Nested) Shapley/Owen (levels) value · Harsanyi dividends 
JEL:  C71 
Date:  2020–03–30 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:99355&r=all 
By:  Takafumi Otsuka 
Abstract:  In this paper, we study the egalitarian solution for games with discrete side payment, where the characteristic function is integervalued and payoffs of players are integral vectors. The egalitarian solution, introduced by Dutta and Ray in 1989, is a solution concept for transferable utility cooperative games in characteristic form, which combines commitment for egalitarianism and promotion of indivisual interests in a consistent manner. We first point out that the nice properties of the egalitarian solution (in the continuous case) do not extend to games with discrete side payment. Then we show that the Lorenz stable set, which may be regarded a variant of the egalitarian solution, has nice properties such as the Davis and Maschler reduced game property and the converse reduced game property. For the proofs we utilize recent results in discrete convex analysis on decreasing minimization on an Mconvex set investigated by Frank and Murota. 
Date:  2020–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2003.10059&r=all 
By:  Yue Feng (School of Business, Nanjing University, China and Center for PostDoctoral Studies, Bank of Nanjing, China); Tarun Sabarwal (Department of Economics, University of Kansas) 
Abstract:  Strategic complements are well understood for normal form games, but less so for extensive form games. There is some evidence that extensive form games with strategic complementarities are a very restrictive class of games (Echenique (2004)). We study necessary and sufficient conditions for strategic complements (defined as increasing best responses) in two stage, 2x2 games. We find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in which payoffs satisfy these conditions has measure zero. Payoffs with these conditions require the player to be indifferent between their actions in two of the four subgames in stage two, eliminating any strategic role for their actions in these two subgames. In contrast, the set of games that exhibit strategic complements (increasing best responses) has infinite measure. This enlarges the scope of strategic complements in two stage, 2x2 games (and provides a basis for possibly greater scope in more general games). The set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice. The results are easy to apply, and are robust to including dual payoff conditions and adding a third player. Examples with several motivations are included. 
Keywords:  Strategic complements, extensive form game, two stage game 
JEL:  C60 C70 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:kan:wpaper:202006&r=all 
By:  A. B. Leoneti; G. A. Prataviera 
Abstract:  Motivated by empirical evidence that individuals within group decision making simultaneously aspire to maximize utility and avoid inequality we propose a criterion based on the entropynorm pair for geometric selection of strict Nash equilibria in nperson games. For this, we introduce a mapping of an nperson set of Nash equilibrium utilities in an EntropyNorm space. We suggest that the most suitable group choice is the equilibrium closest to the largest entropynorm pair of a rescaled EntropyNorm space. Successive application of this criterion permits an ordering of the possible Nash equilibria in an nperson game accounting simultaneously equality and utility of players payoffs. Limitations of this approach for certain exceptional cases are discussed. In addition, the criterion proposed is applied and compared with the results of a group decision making experiment. 
Date:  2020–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2003.09225&r=all 
By:  Elizabeth Baldwin (Dept. of Economics, Oxford University); Paul W. Goldberg (Dept. of Computer Science, Oxford University); Paul Klemperer (Dept. of Economics, Oxford University); Edwin Lock (Dept. of Computer Science, Oxford University) 
Abstract:  This paper develops algorithms to solve strongsubstitutes productmix auctions: it finds competitive equilibrium prices and quantities for agents who use this auction’s bidding language to truthfully express their strongsubstitutes preferences over an arbitrary number of goods, each of which is available in multiple discrete units. Our use of the bidding language, and the information it provides, contrasts with existing algorithms that rely on access to a valuation or demand oracle. We compute marketclearing prices using algorithms that apply existing submodular minimisation methods. Allocating the supply among the bidders at these prices then requires solving a novel constrained matching problem. Our algorithm iteratively simplifies the allocation problem, perturbing bids and prices in a way that resolves tiebreaking choices created by bids that can be accepted on more than one good. We provide practical running time bounds on both pricefinding and allocation, and illustrate experimentally that our allocation mechanism is practical. 
Keywords:  bidding language, productmix auction, competitive equilibrium, Walrasian equilibrium, convex optimisation, strong substitutes, submodular minimisation 
Date:  2019–10–06 
URL:  http://d.repec.org/n?u=RePEc:nuf:econwp:1908&r=all 
By:  Quinteros, María José; Villena, Marcelo J.; Villena, Mauricio G. 
Abstract:  We develop a game theoretical model of whistleblowing behavior in organizations, focusing speci�fically on the role of incentives aimed at encouraging this type of behavior. We also analyze the potential impacts of whistleblowing behavior on the persistence of corruption. First, we present a static game consisting of two employees with three available strategies: honest, corrupt and whistleblowing behavior. Later, we examine the pure and mixed Nash equilibrium strategies of the game. Second, we use the concept of replicator dynamics to formally explore the local asymptotic stability of whistleblowing behavior within organizations. Our main results show that whistleblowing as a mechanism to control wrongdoing is only relevant under the existence of external monitoring (if the probability of detecting wrongdoing with an external mechanism is close to zero, then in the long term, all employees will begin to behave corruptly). We also show that whistleblowers reduce the minimum wages required to avoid corruption within an organization, making it less costly for an organization to combat corruption. Finally, we claim that whistleblowing strategies seem to be less attractive for activities with very high bribery in comparison to the rewards for whistleblowers, for example, this could be the case of manufacturing or retail, but not for �nancial services in general. 
Keywords:  whistleblowing, corruption, game theory, replicator dynamics, incentives. 
JEL:  C73 K4 M12 
Date:  2019–11–24 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:99215&r=all 
By:  Giuseppe Attanasi; Samuele Centorrino; Elena Manzoni 
Abstract:  We study two wellknown electronic markets: an overthecounter (OTC) market, in which each agent looks for the best counterpart through bilateral negotiations, and a double auction (DA) market, in which traders post their quotes publicly. We focus on the DAOTC efficiency gap and show how it varies with different market sizes (10, 20, 40, and 80 traders). We compare experimental results from a sample of 6,400 undergraduate students in Economics and Management with zerointelligent (ZI) agentbased simulations. Simulations with ZI traders show that the traded quantity (with respect to the e cient one) increases with market size under both DA and OTC. Experimental results with human traders confrm the same tendency under DA, while the share of periods in which the traded quantity is higher (lower) than the efficient one decreases (increases) with market size under OTC, ultimately leading to a DAOTC efficiency gap increasing with market size. We rationalize these results by putting forward a novel gametheoretical model of OTC market as a repeated bargaining procedure under incomplete information on buyers' valuations and sellers' costs, showing how efficiency decreases slightly with size due to two counteracting e ects: acceptance rates in earlier periods decrease with size, and earlier offers increase, but not always enough to compensate for the decreasein acceptance rates. 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:nys:sunysb:2004&r=all 
By:  Bogliacino, Francesco; Rodríguez González, Nicolás 
Abstract:  In this article, we study a threeperson gift exchange, where two workers compete for a bonus. We derive the equilibrium properties of the models of sequential reciprocity and inequity aversion. We then prove a comparative statics theorem, when one worker becomes more productive. We show that compared with the predictions of outcome based model, those of the intention based model contrast sharply. This creates an ideal setting in which to perform a controlled experiment to test them. Our results largely support sequential reciprocity. 
Keywords:  Gift exchange; sequential reciprocity; inequity aversion 
JEL:  A13 C72 C91 D63 
Date:  2020–03 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:99055&r=all 
By:  Evan M. Calford; Anujit Chakraborty 
JEL:  D85 D91 C92 
Date:  2020–12 
URL:  http://d.repec.org/n?u=RePEc:pur:prukra:1323&r=all 
By:  Arthur Charpentier; Romuald Elie; Carl Remlinger 
Abstract:  Reinforcement learning algorithms describe how an agent can learn an optimal action policy in a sequential decision process, through repeated experience. In a given environment, the agent policy provides him some running and terminal rewards. As in online learning, the agent learns sequentially. As in multiarmed bandit problems, when an agent picks an action, he can not infer expost the rewards induced by other action choices. In reinforcement learning, his actions have consequences: they influence not only rewards, but also future states of the world. The goal of reinforcement learning is to find an optimal policy  a mapping from the states of the world to the set of actions, in order to maximize cumulative reward, which is a long term strategy. Exploring might be suboptimal on a shortterm horizon but could lead to optimal longterm ones. Many problems of optimal control, popular in economics for more than forty years, can be expressed in the reinforcement learning framework, and recent advances in computational science, provided in particular by deep learning algorithms, can be used by economists in order to solve complex behavioral problems. In this article, we propose a stateoftheart of reinforcement learning techniques, and present applications in economics, game theory, operation research and finance. 
Date:  2020–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2003.10014&r=all 
By:  Samir Wadhwa; Roy Dong 
Abstract:  The advent of machine learning tools has led to the rise of data markets. These data markets are characterized by multiple data purchasers interacting with a set of data sources. Data sources have more information about the quality of data than the data purchasers; additionally, data itself is a nonrivalrous good that can be shared with multiple parties at negligible marginal cost. In this paper, we study the multipleprincipal, multipleagent problem with nonrivalrous goods. Under the assumption that the principal's payoff is quasilinear in the payments given to agents, we show that there is a fundamental degeneracy in the market of nonrivalrous goods. Specifically, for a general class of payment contracts, there will be an infinite set of generalized Nash equilibria. This multiplicity of equilibria also affects common refinements of equilibrium definitions intended to uniquely select an equilibrium: both variational equilibria and normalized equilibria will be nonunique in general. This implies that most existing equilibrium concepts cannot provide predictions on the outcomes of data markets emerging today. The results support the idea that modifications to payment contracts themselves are unlikely to yield a unique equilibrium, and either changes to the models of study or new equilibrium concepts will be required to determine unique equilibria in settings with multiple principals and a nonrivalrous good. 
Date:  2020–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2004.00196&r=all 