Game Theory
http://lists.repec.org/mailman/listinfo/nep-gth
Game Theory
2019-04-08
Decomposition of games: some strategic considerations
http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-02079215&r=gth
Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and non-strategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a game-theoretical point of view, for instance games obtained via duplications of strategies or suitable linear transformations of payoffs. We consider classes of decompositions and show when two decompositions of equivalent games are coherent.
Joseph Abdou
Nikolaos Pnevmatikos
Marco Scarsini
Xavier Venel
Decomposition of games,Potential games,Harmonic games,Duplicate strategies,Gradient operator,Projection operator,Décomposition de jeux,Jeux potentiels,Jeux harmoniques,Stratégies dupliquées,Opérateur gradient,Opérateur de projection
2019-02
The Nucleolus and Inheritance of Properties in Communication Situations
http://d.repec.org/n?u=RePEc:tiu:tiucen:bacc7f47-9b6b-4ce4-9f97-4c80dbaface8&r=gth
This paper studies the nucleolus of graph-restricted games as an alternative for the Shapley value to evaluate communication situations. We focus on the inheritance of properties of cooperative games related to the nucleolus: balancedness (the nucleolus is in the core), compromise stability and strong compromise admissibility (these properties allow for a direct, closed formula for the nucleolus). We characterize the families of graphs for which the graph-restricted games inherit these properties from the underlying games. Moreover, for each of these properties, we characterize the family of graphs for which the nucleolus is invariant.
Schouten, Jop
Dietzenbacher, Bas
Borm, Peter
nucleolus; communication situations; graph-restricted game; inheritance of properties; compormise stability; strong compromise admissibility; invariance
2019
A Generalization of Peleg's Representation Theorem on Constant-Sum Weighted Majority
http://d.repec.org/n?u=RePEc:mei:wpaper:43&r=gth
We propose a variant of the nucleolus associated with distorted satisfaction of each coalition in TU games. This solution is referred to as the α-nucleolus in which α is a profile of distortion rates of satisfaction of all the coalitions. We apply the α-nucleolus to constant-sum weighted majority games. We show that under assumptions of distortions of satisfaction of winning coalitions the α-nucleolus is the unique normalized homogeneous representation of constant-sum weighted majority games which assigns a zero to each null player. As corollary of this result, we derive the well-known Peleg’s representation theorem.
Takayuki Oishi
Constant-sum weighted majority games; Homogeneous representation; α-Nucleolus; Distorted satisfaction; Peleg’s representation theorem
2019-03
A Variational Approach to Network Games
http://d.repec.org/n?u=RePEc:ags:feemth:268732&r=gth
This paper studies strategic interaction in networks. We focus on games of strategic substitutes and strategic complements, and departing from previous literature, we do not assume particular functional forms on players' payoffs. By exploiting variational methods, we show that the uniqueness, the comparative statics, and the approximation of a Nash equilibrium are determined by a precise relationship between the lowest eigenvalue of the network, a measure of players' payoff concavity, and a parameter capturing the strength of the strategic interaction among players. We apply our framework to the study of aggregative network games, games of mixed interactions, and Bayesian network games.
Melo, Emerson
Research Methods/ Statistical Methods
2018-02-26
Bargaining on Supply Chain Networks with Heterogeneous Valuations
http://d.repec.org/n?u=RePEc:tcb:wpaper:1907&r=gth
In this study, a bargaining between buyers and sellers on a stationary two-sided supply chain network is modelled. Any further restrictions on the network structure is not imposed. Both buyers and sellers are allowed to make offers in the bargaining game. Furthermore, valuations of buyers for the good are heterogeneous. The results reveal that the equilibrium payoffs in the bargaining game that we study depend on the valuations of the buyers and the network positions of all players. As such, these two factors turn out to be the main sources of bargaining power.
Elif Ozcan Tok
Bargaining, Heterogeneity, Networks, Supply chain
2019
Persistence of Power: Repeated Multilateral Bargaining with Endogenous Agenda Setting Authority
http://d.repec.org/n?u=RePEc:qed:wpaper:1414&r=gth
In models of dynamic multilateral bargaining, the literature tends to focus on stationary subgame perfect or stationary Markov perfect equilibria, which restrict attention to forward-looking, history-independent strategies. Evidence supporting such refinements come from environments in which proposal power is exogenous and the incentives for players to develop cooperative relationships are minimized. However, in many environments including legislative bargaining, agenda-setting power is endogenous and it is commonplace for players to form coalitions and establish reputations. Through a series of lab experiments, we show that in repeated environments, standard equilibrium refinements may predict some aspects of the data when outcomes when proposal power is randomly assigned, but do not predict outcomes when proposal power is endogenous.
Marina Agranov
Christopher Cotton
Chloe Tergiman
legislative bargaining, laboratory experiment, history independence, repeated games
2019-03
Game of Variable Contributions to the Common Good under Uncertainty
http://d.repec.org/n?u=RePEc:arx:papers:1904.00500&r=gth
We consider a stochastic game of contribution to the common good in which the players have continuous control over the degree of contribution, and we examine the gradualism arising from the free rider effect. This game belongs to the class of variable concession games which generalize wars of attrition. Previously known examples of variable concession games in the literature yield equilibria characterized by singular control strategies without any delay of concession. However, these no-delay equilibria are in contrast to mixed strategy equilibria of canonical wars of attrition in which each player delays concession by a randomized time. We find that a variable contribution game with a single state variable, which extends the Nerlove-Arrow model, possesses an equilibrium characterized by regular control strategies that result in a gradual concession. This equilibrium naturally generalizes the mixed strategy equilibria from the canonical wars of attrition. Stochasticity of the problem accentuates the qualitative difference between a singular control solution and a regular control equilibrium solution. We also find that asymmetry between the players can mitigate the inefficiency caused by the gradualism.
H. Dharma Kwon
2019-03
Waiting for my Neighbors
http://d.repec.org/n?u=RePEc:spo:wpecon:info:hdl:2441/3lcrvb72lq9f08o6s7j1m8j4d7&r=gth
We introduce a neighborhood structure in a waiting game, where the payoff of stopping increases each time a neighbor stops. We show that the dynamic evolution of the network depends on initial parameters and can take the form of either a shrinking network, where players at the edges stop first, or a fragmenting network where interior players stop first. We find that, in addition to the coordination inefficiency standard in waiting games, the neighborhood structure gives rise to two other inefficiencies, the first linked to the order of exit and the second to the final distribution of remaining nodes.
Sidartha Gordon
Emeric Henry
Pauli Murto
Waiting games; Networks; Inefficiencies
2018-08
Information Design In Coalition Formation Games
http://d.repec.org/n?u=RePEc:ags:feemth:258010&r=gth
I examine a setting, where an information sender conducts research into a payoff-relevant state variable, and releases information to agents, who consider joining a coalition. The agents' actions can cause harm by contributing to a public bad. The sender, who has commitment power, by designing an information mechanism (a set of signals and a probability distribution over them), maximises his payoff, which depends on the action taken by the agents, and the state variable. I show that the coalition size, as a function of beliefs of agents, is an endogenous variable, induced by the information sender. The optimal information mechanism from the general set of public information mechanisms, in coalition formation games is derived. I also apply the results to International Environmental Agreements (IEAs), where a central authority, as an information sender, attempts to reduce the global level of greenhouse gases (GHG) by communication of information on social cost of GHG.
Sareh Vosooghi
Research Methods/ Statistical Methods
2017-06-23
Warm-Glow Giving in Networks with Multiple Public Goods
http://d.repec.org/n?u=RePEc:ags:feemth:259480&r=gth
This paper explores a voluntary contribution game in the presence of warm-glow effects. There are many public goods and each public good benefits a different group of players. The structure of the game induces a bipartite network structure, where players are listed on one side and the public good groups they form are listed on the other side. The main result of the paper shows the existence and uniqueness of a Nash equilibrium. The unique Nash equilibrium is also shown to be locally asymptotically stable. Then the paper provides some comparative statics analysis regarding pure redistribution, taxation and subsidies. It appears that small redistributions of wealth may sometimes be neutral, but generally, the effects of redistributive policies depend on how public good groups are related in the contribution network structure.
Richefort, Lionel
Research Methods/ Statistical Methods
2017-07-13
Market power and information effects in a multi-unit auction
http://d.repec.org/n?u=RePEc:zur:econwp:320&r=gth
We study the effects of different information structures (full information, supply uncertainty and demand uncertainty) on equilibrium prices, allocative efficiency and bidding behavior in a (supply-side) uniform-price multi-unit auction, using supply function competition and a novel experimental design. Our setup integrates different types of market power and a varying level of competition. We empirically find that average prices tend to be higher under full information compared to the cases where bidders either have limited information about about the demand level or rivals’ technologies or; the latter even leading to strictly lower average prices as the exertion of market power and bid shading is strongly reduced. We explain this finding with a behavioral equilibrium concept, where bidders behave as if competing against the average market situation. Further, we address the problem of multiplicity of equilibria by exploiting the equilibrium conditions to obtain an empirical selection of the average equilibrium supply function. The respective predictions of the average prices exceed those by standard OLS in all information treatments.
Andreas Hefti
Peiyao Shen
Regina Betz
Multi-unit auctions, limited information, market power, supply function competition, supply uncertainty, demand uncertainty, restricted least squares
2019-03
Search without observability
http://d.repec.org/n?u=RePEc:syd:wpaper:2019-04&r=gth
We analyze a search game in which multiple agents search an area (an island) for a hidden prize of known value. In every period until discovery, the rivals decide where and how much of the unsearched island to explore. The game ends when a player or players discover the prize. If one player discovers the prize on their own, they alone enjoy the spoils. Players have a per-period discount factor and costs proportional to how much they search. We compare two cases when: (i) the search of rivals (past and present) is observable to all; and (ii) players cannot observe others’ previous and current search. We show that welfare in the unique SMPE with observability is always (weakly) higher than in the case without observability. However, we show that there is a self-enforcing mechanism without observability in which a third party ex ante allocates search zones to each of the players that ensures the same outcome is achievable as with observability. Our results have implications for the design of search games (patents, prizes, information sharing, and so on) by regulators.
Matros, Alexander
Ponomareva, Natalia
Smirnov, Vladimir
Wait, Andrew
search; uncertainty; regulatory design.
2019-03
Theory of Mind and Strategic Decision-Making
http://d.repec.org/n?u=RePEc:wrk:warwec:1191&r=gth
In a laboratory experiment, 338 participants were asked to communicate in pairs and then play two games with their partners: the 11-20 money request game (a tool for assessing level-k reasoning) and a public goods game. The communication occurred prior to any knowledge of what was to follow but played an important role in allowing them to develop theories or mental models of their partners (“theory of mind”) which proved to be crucial explanatory factors for decision-making. We examine the players’ beliefs about the personality and intelligence of their partner, how they play in the games and analysed the language used during communication. The results indicate that beliefs about partner’s type is biased by own-type. In particular, extraverts, characterised by positive affect, projected their positivity onto their partners. The level-k strategy chosen in the 11-20 game increased with the perceived similarity between players and in the public goods game, players cooperated more when they believed their partners to be extraverted. An analysis of the text used during communication explains how it was possible for participants to draw inferences about other’s type: for instance, use of more words and more dominant words were associated with being an extravert.
Bose, Neha
Sgroi, Daniel
theory of mind ; cheap talk ; communication ; level-k reasoning ; public goods game ; cooperation ; extraversion ; perceived similarity ; self-projection bias ; laboratory experiment ; text analysis.
2019
Our distrust is very expensive
http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-632&r=gth
Motivated by reputation management in a variety of different markets for ``expertise'' (such as online content providers and experts in organizations), we develop a novel repeated-game framework in which a principal screens a strategic agent whose type determines the rate at which he privately receives payoff relevant information. The stage game is a bandit setting, where the principal chooses whether or not to experiment with a risky arm which is controlled by an agent who privately knows its type. Irrespective of type, the agent strategically chooses output from the arm to maximize the duration of experimentation. Experimentation is only potentially valuable to the principal if the arm is of the high type. Our main insight is that reputational incentives can be exceedingly strong: the agent makes inefficient output choices in all equilibria (subject to a mild refinement) and that this can result in market breakdown even when the uncertainty about the agent's type is arbitrarily small. We show that (one-sided) transfers do not prevent this inefficiency and we suggest alternate ways to improve the functioning of these markets.
Rahul Deb
Matthew Mitchell
Mallesh Pai
reputation, repeated games of imperfect public monitoring, relational contracting, strategic experimentation, markets for expertise, media
2019-03-22
Self-Enforcing International Environmental Agreements: Adaptation and Complementarity
http://d.repec.org/n?u=RePEc:ags:feemth:276179&r=gth
This paper studies the impact of adaptation on the stability of an international emission agreement. To address this issue we solve a three-stage coalition formation game where in the first stage countries decide whether or not to sign the agreement. Then, in the second stage, signatories (playing together) and non-signatories (playing individually) select their levels of emissions. Finally, in the third stage, each country decides on its level of adaptation non co-operatively. We solve this game for two models. For both, it is assumed that damages are linear with respect to emissions which guarantee that emissions are strategic complements in the second stage of the game. However, for the first model adaptation reduces the marginal damages of emissions in a multiplicative way whereas for the second model the reduction occurs in an additive way. Our analysis shows that the models yield different predictions in terms of participation. In the first case, we find that the larger the gains of full cooperation, the larger the cooperation. However, in the second case, the unique stable agreement we find consists of three countries regardless of the gains of full cooperation. These results suggest that complementarity can play in favor of cooperation but that it is not a sufficient condition to obtain more participation in an emission agreement. Finally, we would like to point out that our research indicates that the way adaptation reduces damages plays a critical role over the outcome of the coalition formation game.
Rubio, Santiago J.
Research Methods/ Statistical Methods
2018-08-31
Contagion in Stable Networks
http://d.repec.org/n?u=RePEc:ags:feemth:263489&r=gth
We study the formation of networks in environments where agents derive benefits from other agents directly linked to them but suffer losses through contagion when any agent on a path connected to them is hit by a shock. We first consider networks with undirected links (e.g. epidemics, underground resistance organizations, trade networks) where we find that stable networks are comprised of completely connected disjoint subnetworks. Then, we consider networks with directed links and we find that the completely connected network is stable, although, its exact structure, and thus contagion implications, is sensitive to parameter values for costs and benefits. Lastly, we introduce aggregate externalities (e.g. fire sales for the case of financial networks) and we find that stable networks can be asymmetric, connected but not completely connected, thus capturing the main features of inter-industry and financial networks.
Bougheas, Spiros
Research Methods/ Statistical Methods
2017-09-25
Bi and Branching Strict Nash Networks in Two-way Flow Models: a Generalized Sufficient Condition
http://d.repec.org/n?u=RePEc:ags:feemth:273140&r=gth
Bi and branching networks are two classes of minimal networks often found in the literatures of two-way flow Strict Nash networks. Why so? In this paper, we answer this question by establishing a generalized condition that holds together many models in the literature, and then show that this condition is sufficient to guarantee their common result: every non-empty component of minimal SNN is either a branching or Bi network. This paper, therefore, contributes to the literature by providing a generalization of several existing works in the literature of two-way flow Strict Nash networks.
Charoensook, Banchongsan
Research Methods/ Statistical Methods
2018-05-24
Network Formation in Large Groups
http://d.repec.org/n?u=RePEc:cam:camdae:1935&r=gth
We conduct an experiment to understand the principles that govern network formation. The design of the experiment builds on a model of linking and efforts taken from Galeotti and Goyal [2010]. In order to reduce cognitive complexity facing human subjects and facilitate learning, we develop a new experimental platform that integrates a network visualization tool using an algorithm of Barnes and Hut [1986] with an interactive tool of asynchronous choices in continuous time. Our experiment provides strong support for macroscopic predictions of the theory: there is specialization in linking and efforts across all treatments. Moreover, and in line with the theory, the specialization is more pronounced in larger groups. Thus subjects abide by the law of the few. Information on payoffs provided to subjects affects their behavior and yields differential welfare consequences. In the treatment where subjects see only their own payoffs, in large groups, the most connected individuals compete fiercely-they exert large efforts and have small earnings. By contrast, when a subject sees everyone's payoffs, in large groups, the most connected individuals engage in less intense competition-they exert little effort and have large earnings. The effects of information are much more muted in small groups.
Choi, S
Goyal, S.
Moisan, F.
2019-03-28
Matching with Myopic and Farsighted Players
http://d.repec.org/n?u=RePEc:ags:feemth:259484&r=gth
We study stable sets for marriage problems under the assumption that players can be both myopic and farsighted. We introduce the new notion of the myopic-farsighted stable set. For the special cases where all players are myopic and where all players are farsighted, our concept predicts the set of matchings in the core. When all men are myopic and the top choice of each man is a farsighted woman, we show that the singleton consisting of the woman-optimal stable matching is a myopic-farsighted stable set. The same result holds when all women are farsighted.
Herings, P. Jean-Jacques
Mauleon; Ana
Vincent Vannetelbosch, Vincent
Research Methods/ Statistical Methods
2017-07-13
Farsighted Stability with Heterogeneous Expectations
http://d.repec.org/n?u=RePEc:ags:feemth:259479&r=gth
This paper analyzes farsighted stable sets when agents have heterogeneous expectations over the dominance paths. We consider expectation functions satisfying two properties of path-persistence and consistency. We show that farsighted stable sets with heterogeneous expectations always exist and that any singleton farsighted stable set with common expectations is a farsighted stable set with heterogeneous expectations. We characterize singleton farsighted stable sets with heterogeneous expectations in one-to-one matching models and voting models, and show that the relaxation of the hypothesis of common expectations greatly expands the set of states that can be supported as singleton farsighted stable sets.
Francis Bloch
Anne van den Nouweland
Research Methods/ Statistical Methods
2017-07-13
A family of rules to share the revenues from broadcasting sport events
http://d.repec.org/n?u=RePEc:pab:wpaper:19.07&r=gth
We consider the problem of sharing the revenues from broadcasting sport league events, introduced by Bergantiños and Moreno-Ternero (2019). We characterize a family of rules compromising between two focal and somewhat polar rules: the equal-split rule and concede-and-divide}. The characterization only makes use of three basic axioms: equal treatment of equals}, additivity and maximum aspirations}}. We also show further interesting features of the family: (i) if we allow teams to vote for any rule within the family, then a majority voting equilibrium exists; (ii) the rules within the family yield outcomes that are fully ranked according to the Lorenz dominance criterion; (iii) the family provides rationale for existing schemes in real-life situations.
Gustavo Bergantiños
Juan D. Moreno-Ternero
resource allocation, broadcasting, sport events, concede-and-divide, Shapley value
2019-03
Distributed Mechanism Design for Network Resource Allocation Problems
http://d.repec.org/n?u=RePEc:arx:papers:1904.01222&r=gth
In the standard Mechanism Design framework, agents' messages are gathered at a central point and allocation/tax functions are calculated in a centralized manner, i.e., as functions of all network agents' messages. This requirement may cause communication and computation overhead and necessitates the design of mechanisms that alleviate this bottleneck. We consider a scenario where message transmission can only be performed locally so that the mechanism allocation/tax functions can be calculated in a decentralized manner. Each agent transmits messages to her local neighborhood, as defined by a given message-exchange network, and her allocation/tax functions are only functions of the available neighborhood messages. This scenario gives rise to a novel research problem that we call "Distributed Mechanism Design". In this paper, we propose two distributed mechanisms for network utility maximization problems that involve private and public goods with competition and cooperation between agents. As a concrete example, we use the problems of rate allocation in networks with either unicast or multirate multicast transmission protocols. The proposed mechanism for each of the protocols fully implements the optimal allocation in Nash equilibria and its message space dimensionality scales linearly with respect to the number of agents in the network.
Nasimeh Heydaribeni
Achilleas Anastasopoulos
2019-04
Collusive Agreements in Vertically Differentiated Markets
http://d.repec.org/n?u=RePEc:ags:feemth:258011&r=gth
This paper introduces a number of game-theoretic tools to model collusive agreements among firms in vertically differentiated markets. I firstly review some classical literature on collusion between two firms producing goods of exogenous different qualities. I then extend the analysis to a n-firm vertically differentiated market to study the incentive to form either a whole market alliance or partial alliances made of subsets of consecutive firms in order to collude in prices. Within this framework I explore the price behaviour of groups of colluding firms and their incentive to either pruning or proliferating their products. It is shown that a selective pruning within the cartel always occurs. Moreover, by associating a partition function game to the n-firm vertically differentiated market, it can be shown that a sufficient condition for the cooperative (or coalitional) stability of the whole industry cartel is the equidistance of firms’ products along the quality spectrum. Without this property, and in presence of large quality differences, collusive agreements easily lose their stability. In addition, introducing a standard infinitely repeated-game approach, I show that an increase in the number of firms in the market may have contradictory effects on the incentive of firms to collude: it can make collusion easier for bottom and intermediate firms and harder for the top quality firm. Finally, by means of a three-firm example, I consider the case in which alliances can set endogenously qualities, prices and number of variants on sale. I show that, in every formed coalition, (i) market pruning dominates product proliferation and (ii) partial cartelisation always arises in equilibrium, with the bottom quality firm always belonging to the alliance.
Marco A. Marini
Research Methods/ Statistical Methods
2017-06-23
Commuting and internet traffic congestion
http://d.repec.org/n?u=RePEc:pra:mprapa:92962&r=gth
We examine the fine microstructure of commuting in a game-theoretic setting with a continuum of commuters. Commuters' home and work locations can be heterogeneous. A commuter transport network is exogenous. Traffic speed is determined by link capacity and by local congestion at a time and place along a link, where local congestion at a time and place is endogenous. The model can be reinterpreted to apply to congestion on the internet. We find sufficient conditions for existence of equilibrium, that multiple equilibria are ubiquitous, and that the welfare properties of morning and evening commute equilibria differ on a tree.
Berliant, Marcus
Commuting; Internet traffic; Congestion externality; Efficient Nash equilibrium
2019-03-25
Uncertainty and Risk-aversion in a Dynamic Oligopoly with Sticky Prices
http://d.repec.org/n?u=RePEc:ags:feemth:285025&r=gth
In this paper we present a dynamic discrete-time model that allows to investigate the impact of risk-aversion in an oligopoly characterized by a homogeneous non-storable good, sticky prices and uncertainty. Our model nests the classical dynamic oligopoly model with sticky prices by Fershtman and Kamien (Fershtman and Kamien, 1987), which can be viewed as the continuous-time limit of our model with no uncertainty and no risk-aversion. Focusing on the continuous-time limit of the infinite horizon formulation we show that the optimal production strategy and the consequent equilibrium price are, respectively, directly and inversely related to the degrees of uncertainty and risk-aversion. However, the effect of uncertainty and risk-aversion crucially depends on price stickiness since, when prices can adjust instantaneously, the steady state equilibrium in our model with uncertainty and risk aversion collapses to Fershtman and Kamien’s analogue.
Valentini, Edilio
Vitale, Paolo
Research Methods/ Statistical Methods
2019-03-19
Tragedy of the Commons and Evolutionary Games in Social Networks: The Economics of Social Punishment
http://d.repec.org/n?u=RePEc:ags:feemth:259486&r=gth
This study revisits the problem of the tragedy of the commons. Extracting agents participate in an evolutionary game in a complex social network and are subject to social pressure if they do not comply with the social norms. Social pressure depends on the dynamics of the resource, the network and the population of compliers. We analyze the influence the network structure has on the agents’ behavior and determine the economic value of the intangible good - social pressure. For a socially optimal management of the resource, an initially high share of compliers is necessary but is not sufficient. The analysis shows the extent to which the remaining level of the resource, the share of compliers and the size, density and local cohesiveness of the network contribute to overcoming the tragedy of the commons. The study suggests that the origin of the problem – shortsighted behavior - is also the starting point for a solution in the form of a one-time payment. A numerical analysis of a social network comprising 7500 agents and a realistic topological structure is performed using empirical data from the western La Mancha aquifer in Spain.
Marco, Jorge
Goetz, Renan
Research Methods/ Statistical Methods
2017-07-13