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Similar Journals
 International Journal of Game TheoryJournal Prestige (SJR): 0.564 Number of Followers: 3      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1432-1270 - ISSN (Online) 0020-7276 Published by Springer-Verlag  [2469 journals]
• On $$\alpha$$ α -constant-sum games

Abstract: Given any $$\alpha \in [0,1]$$ , an $$\alpha$$ -constant-sum game (abbreviated as $$\alpha$$ -CS game) on a finite set of players, N, is a function that assigns a real number to any coalition $$S\subseteq N$$ , such that the sum of the worth of the coalition S and the worth of its complementary coalition $$N\backslash S$$ is $$\alpha$$ times the worth of the grand coalition. This class contains the constant-sum games of Khmelnitskaya (Int J Game Theory 32:223–227, 2003) (for $$\alpha = 1$$ ) and games of threats of (Kohlberg and Neyman, Games Econ Behav 108:139–145, 2018) (for $$\alpha = 0$$ ) as special cases. An $$\alpha$$ -CS game may not be a classical TU cooperative game as it may fail to satisfy the condition that the worth of the empty set is 0, except when $$\alpha =1$$ . In this paper, we (i) extend the $$\alpha$$ -quasi-Shapley value giving the Shapley value for constant-sum games and quasi-Shapley-value for threat games to any class of $$\alpha$$ -CS games, (ii) extend the axiomatizations of Khmelnitskaya (2003) and Kohlberg and Neyman (2018) to any class of $$\alpha$$ -CS games, and (iii) introduce a new efficiency axiom which, together with other classical axioms, characterizes a solution that is defined by exactly the Shapley value formula for any class of $$\alpha$$ -CS games.
PubDate: 2022-06-01

• Ordinal imitative dynamics

Abstract: This paper introduces an evolutionary dynamics based on imitate the better realization (IBR) rule. Under this rule, an agent in a population game imitates the strategy of a randomly chosen opponent whenever the opponent’s realized payoff is higher than his or her own. Such behavior generates a mean dynamics which depends on the order of payoffs, but not their magnitudes, and is polynomial in strategy utilization frequencies. We demonstrate that while the dynamics does not possess Nash stationarity or payoff monotonicity, under it pure strategies iteratively strictly dominated by pure strategies are eliminated and strict equilibria are locally stable. We investigate the relationship between the dynamics based on the IBR rule and the replicator dynamics. In trivial cases, the two dynamics are topologically equivalent. In Rock-Paper-Scissors games we conjecture that both dynamics exhibit the same types of behavior, but the partitions of the game set do not coincide. In other cases, the IBR dynamics exhibits behaviors that are impossible under the replicator dynamics.
PubDate: 2022-06-01

• The allocation of marginal surplus for cooperative games with transferable
utility

Abstract: Marginal contribution is a significant index to measure every player’s ability to cooperate in cooperative games. Several solutions for cooperative games are defined in terms of marginal contribution, including the Shapley value and the Solidarity value. In this paper, we introduce marginal surplus as an alternative index to describe the contribution level of every player. We define a new solution for cooperative games, namely the average-surplus value, which is determined by an underlying procedure of sharing marginal surplus. Then we characterize the average-surplus value by introducing the A-null surplus player property and the revised balanced contributions property. We also propose the AS-potential function to implement the average-surplus value. Finally, we provide a non-cooperative game, the outcome of which coincides with the average-surplus value in subgame perfect equilibria.
PubDate: 2022-06-01

• The Lipschitz constant of perturbed anonymous games

Abstract: The Lipschitz constant of a game measures the maximal amount of influence that one player has on the payoff of some other player. The worst-case Lipschitz constant of an n-player k-action $$\delta$$ -perturbed game, $$\lambda (n,k,\delta )$$ , is given an explicit probabilistic description. In the case of $$k\ge 3$$ , it is identified with the passage probability of a certain symmetric random walk on $${\mathbb {Z}}$$ . In the case of $$k=2$$ and n even, $$\lambda (n,2,\delta )$$ is identified with the probability that two i.i.d. binomial random variables are equal. The remaining case, $$k=2$$ and n odd, is bounded through the adjacent (even) values of n. Our characterization implies a sharp closed-form asymptotic estimate of $$\lambda (n,k,\delta )$$ as $$\delta n /k\rightarrow \infty$$ .
PubDate: 2022-06-01

• Hart–Mas-Colell consistency and the core in convex games

Abstract: This paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.
PubDate: 2022-06-01

• Intervention with limited information

Abstract: We study how optimal interventions in response to a shock with limited information depend on the complexity of the system. We show that as the complexity of the system grows, the optimal intervention shrinks to zero.
PubDate: 2022-06-01

• On the relationship between p-dominance and stochastic stability in
network games

Abstract: This paper examines the properties of networks that determine the uniqueness of long-run equilibria emerging from symmetric coordination games when players are myopic best responders. We identify the contagion threshold and the network diameter as two measures of finite networks that determine when strategies in the minimal p-best response set of a coordination game are uniquely stochastically stable. We show that when the contagion threshold is greater or equal to p, strategies in the minimal p-best response set are uniquely stochastically stable in strongly connected networks with diameter greater or equal to seven. The contagion threshold and the network diameter are easy to compute and their values are unique for every strongly connected network.
PubDate: 2022-06-01

• The priority value for cooperative games with a priority structure

Abstract: We study cooperative games with a priority structure modeled by a poset on the agent set. We introduce the Priority value, which splits the Harsanyi dividend of each coalition among the set of its members over which no other coalition member has priority. This allocation shares many desirable properties with the classical Shapley value: it is efficient, additive and satisfies the null agent axiom. We provide two axiomatic characterizations of the Priority value which invoke both classical axioms and new axioms describing the effects of the priority structure on the payoff allocation. Finally, in the special case where agents are ranked by level, a link between the Priority value, the weighted Shapley values and the Owen-type values can be drawn.
PubDate: 2022-06-01

• Object reallocation problems under single-peaked preferences: two
characterizations of the crawler

Abstract: In object reallocation problems, if preferences are strict but otherwise unrestricted, TTC is the leading rule: It is the only rule satisfying efficiency, the endowment lower bound, and strategy-proofness. However, on the subdomain of single-peaked preferences, Bade (J Econ Theory 180:81–99, 2019) defines a new rule, the “crawler”, which also satisfies these properties, and in fact enjoys a stronger strategic property. We identify additional interesting properties that the crawler satisfies, and provide two characterizations of this rule. The first characterization is based on the endowment lower bound and two invariance properties, “adjacent-endowment-swapping invariance” and “separability”. The second characterization is based on the endowment lower bound, strategy-proofness, adjacent-endowment-swapping invariance, and another invariance property, “non-bossiness”.
PubDate: 2022-03-15
DOI: 10.1007/s00182-022-00803-6

• An epistemic approach to explaining cooperation in the finitely repeated
Prisoner’s Dilemma

Abstract: We use epistemic game theory to explore rationales behind cooperative behaviors in the finitely repeated Prisoner’s Dilemma. For a class of type structures that are sufficiently rich, the set of outcomes that can arise when each player i is rational and satisfies $$(m_i-1)$$ th order strong belief of rationality is the set of paths on which each player i defects in the last $$m_i$$ rounds. We construct one sufficiently rich type structure to elaborate on how different patterns of cooperative behaviors arise under sufficiently weak epistemic conditions. In this type structure, the optimality of forgiving the opponent’s past defection and the belief that one’s defection will be forgiven account for the richness of the set of behavior outcomes.
PubDate: 2022-03-01
DOI: 10.1007/s00182-021-00785-x

• Existence of value for a differential game with asymmetric information and
signal revealing

Abstract: In the present paper, we investigate the existence of value for a new class of infinite horizon two-person zero-sum differential games with asymmetric information on the random pay-off. Before the game begins, both players receive private information about the randomly chosen running cost, while during the game a public signal dependent of the cost function is generated and observed by both players. We prove that, with suitable notion of strategies, the game has a value, and its value function is the unique bounded continuous viscosity solution of a Hamilton–Jacobi–Isaacs equation.
PubDate: 2022-03-01
DOI: 10.1007/s00182-021-00790-0

• Cyclical behavior of evolutionary dynamics in coordination games with
changing payoffs

Abstract: The paper presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how, for a population of myopic agents with homogeneous preferences, changes in the environment caused by current aggregate behavior may affect future payoffs and hence alter future behavior. The interaction between the agents is based on a symmetric two-strategy game with positive externalities and negative feedback from aggregate behavior to payoffs, so that at every point in time the population has an incentive to coordinate, whereas over time the more popular strategy becomes less appealing. Under the best response dynamics and the logit dynamics with small noise levels the joint trajectories of preferences and behavior converge to closed orbits around the unique steady state, whereas for large noise levels the steady state of the logit dynamics becomes a sink. Under the replicator dynamics the unique steady state of the system is repelling and the trajectories are unbounded unstable spirals.
PubDate: 2022-03-01
DOI: 10.1007/s00182-021-00783-z

• Some remarks on the modeling of discrete matching markets

Abstract: This paper shows that the college admissions model with responsive preferences is not always satisfactory for representing real college admissions markets. Simple examples are used to illustrate real situations, in which the knowledge of the preferences of the institutions over all possible assignments of candidates is necessary for the analysis of relevant problems for the markets under consideration.
PubDate: 2022-03-01
DOI: 10.1007/s00182-021-00788-8

• Some new results on generalized additive games

Abstract: A Generalized Additive Game (GAG) (Cesari et al. in Int J Game Theory 46(4):919–939, 2017) is a Transferable Utility (TU) game (N, v), where each player in N is provided with an individual value, and the worth v(S) of a coalition $$S \subseteq N$$ is obtained as the sum of the individual values of players in another subset $$\mathcal {M}(S)\subseteq N$$ . Based on conditions on the map $$\mathcal {M}$$ (which associates to each coalition S a set of beneficial players $$\mathcal {M}(S)$$ not necessarily included in S), in this paper we characterize classes of GAGs that satisfy properties like monotonicity, superadditivity, (total) balancedness, PMAS-admissibility and supermodularity, for all nonnegative vectors of individual values. We also illustrate the application of such conditions on $$\mathcal {M}$$ over particular GAGs studied in the literature (e.g., glove games (Shapley and Shubik in Int Econ Rev 10:337–362, 1969), generalized airport games (Norde et al. in Eur J Oper Res 136(3):635–654, 2002), fixed tree games (Bjørndal et al. in Math Methods Oper Res 59(2):249–270, 2004), link-connection games (Moretti in Multi-agent systems and agreement technologies, vol 10767. Springer, Cham, 2008; Nagamochi et al. in Math Oper Res 22(1):146–164, 1997), simple minimum cost spanning tree games (Norde et al. in Eur J Oper Res 154(1):84–97, 2004; Tijs et al. in Eur J Oper Res 175(1):121–134, 2006) and graph coloring games (Deng et al. in Math Program 87(3):441–452, 2000; Hamers et al. in Math Program 145(1–2):509–529, 2014)).
PubDate: 2022-03-01
DOI: 10.1007/s00182-021-00786-w

• Nash blocks

Abstract: A product set of pure strategies is a Nash block if it contains all best replies to the Nash equilibria of the game in which the players are restricted to the strategies in the block. This defines an intermediate block property, between curb (Basu and Weibull, Econ Lett 36(2):141–146, https://doi.org/10.1016/0165-1765(91)90179-O, http://www.sciencedirect.com/science/article/pii/016517659190179O, 1991) and coarse tenability (Myerson and Weibull (2015) Econometrica 83(3):943–976, https://doi.org/10.3982/ECTA11048). While the new concept is defined without reference to the consideration-set framework that defines tenability, the framework can be used to characterize Nash blocks in terms of potential conventions when large populations of individuals recurrently interact. Although weaker than curb, Nash blocks nevertheless maintain several robustness properties of curb sets. For example, every Nash block contains an essential component and is robust against payoff perturbations.
PubDate: 2022-03-01
DOI: 10.1007/s00182-021-00784-y

• Simplified group activity selection with group size constraints

Abstract: Several real-world situations can be represented in terms of agents that have preferences over activities in which they may participate. Often, the agents can take part in at most one activity (for instance, since these take place simultaneously), and there are additional constraints on the number of agents that can participate in an activity. In such a setting, we consider the task of assigning agents to activities in a reasonable way. We introduce the simplified group activity selection problem providing a general yet simple model for a broad variety of settings, and start investigating its special case where upper and lower bounds of the groups have to be taken into account. We apply different solution concepts such as envy-freeness and core stability to our setting and provide a computational complexity study for the problem of finding such solutions.
PubDate: 2022-03-01
DOI: 10.1007/s00182-021-00789-7

• The equal collective gains value in cooperative games

Abstract: The property of equal collective gains means that each player should obtain the same benefit from the cooperation of the other players in the game. We show that this property jointly with efficiency characterize a new solution, called the equal collective gains value (ECG-value). We introduce a new class of games, the average productivity games, for which the ECG-value is an imputation. For a better understanding of the new value, we also provide four alternative characterizations of it, and a negotiation model that supports it in subgame perfect equilibrium.
PubDate: 2022-03-01
DOI: 10.1007/s00182-021-00791-z

• Optimal contracts with random monitoring

Abstract: We study an optimal contract problem under moral hazard in a principal-agent framework where contracts are implemented through random monitoring. This is a monitoring instrument that reveals the precise action taken by the agent with some nondegenerate probability, and otherwise reveals no information. The agent’s cost of performing the action depends on a random state of nature. This state is private information to the agent, but can be non-verifiably communicated, allowing the contract to specify wages as a function of the agent’s message. We show that the optimal contract partitions the set of types in three regions. The most efficient types exert effort and receive a reward when monitored. Moderately efficient types exert effort but are paid the same wage with monitoring as without. The least efficient types do not exert effort. More intense monitoring increases the value of a contract when the agent is risk averse.
PubDate: 2022-03-01
DOI: 10.1007/s00182-021-00787-9

• Coordination on networks with farsighted and myopic agents

Abstract: We study a coordination game on a fixed connected network where players have to choose between two projects. Some players are moderate (i.e. they are ex-ante indifferent between both projects) while others are stubborn (i.e. they always choose the same project). Benefits for moderate players are increasing in the number of neighbors who choose the same project. In addition, players are either farsighted or myopic. Farsighted players anticipate the reactions of others while myopic players do not. We show that, when all players are farsighted, full coordination among the moderate players is reached except if there are stubborn players for both projects. When the population is mixed, the set of stable strategy profiles is a refinement of the set of Nash equilibrium strategy profiles. In fact, turning myopic players into farsighted ones eliminates gradually the inefficient Nash equilibria. Finally, we consider a social planner who can improve coordination by means of two policy instruments: adding links to the network (socialization) and/or turning myopic players into farsighted ones (education).
PubDate: 2022-01-09
DOI: 10.1007/s00182-021-00802-z

• Fairness and fuzzy coalitions

Abstract: In this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.
PubDate: 2021-12-01
DOI: 10.1007/s00182-021-00780-2

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