Payoffs Of Players Research Articles

A Unique and Stable $$\hbox {Se}{\mathcal {C}}\hbox {ure}$$ Se C ure Reversion Protocol Improving Efficiency: A Computational Bayesian Approach for Empirical Analysis

In Bayesian mechanism we demonstrate the unicity and the stability of secure reversion protocols in which risk-averse players have no incentive to cheat or to deviate from the meditator’s recommendation and that can greatly improve their equilibrium expected payoffs as compared to those generated through correlation device. The main idea of this work is to show the ease with which we can compute the equilibrium expected payoffs for players. Furthermore, we emphasize those results through a numerical simulation for which the method is able to be used for empirical analysis.

Interaction times change evolutionary outcomes: Two-player matrix games

Two most influential models of evolutionary game theory are the Hawk-Dove and Prisoner's dilemma models. The Hawk-Dove model explains evolution of aggressiveness, predicting individuals should be aggressive when the cost of fighting is lower than its benefit. As the cost of aggressiveness increases and outweighs benefits, aggressiveness in the population should decrease. Similarly, the Prisoner's dilemma models evolution of cooperation. It predicts that individuals should never cooperate despite cooperation leading to a higher collective fitness than defection. The question is then what are the conditions under which cooperation evolves? These classic matrix games, which are based on pair-wise interactions between two opponents with player payoffs given in matrix form, do not consider the effect that conflict duration has on payoffs. However, interactions between different strategies often take different amounts of time. In this article, we develop a new approach to an old idea that opportunity costs lost while engaged in an interaction affect individual fitness. When applied to the Hawk-Dove and Prisoner's dilemma, our theory that incorporates general interaction times leads to qualitatively different predictions. In particular, not all individuals will behave as Hawks when fighting cost is lower than benefit, and cooperation will evolve in the Prisoner's dilemma.

Extended Warranty: An Approach via Stackelberg Game

This paper aims at showing how the game theory can be applied to the quantitative study of extended warranty (EW). This kind of after-sales service represents an additional noncompulsory coverage, which the consumer can or not buy after the acquisition of some device, starting subsequently to the end of the base warranty (BW) period. Thus, a model, in which two players interact, is shown, i. e. the original equipment manufacturer (OEM), in charge of assigning prices to the equipment and to the extended warranty service; and the customer (owner of the device). The way, in which the parts interact, is modeled through the Stackelberg leadership game, which was originally applied in the analysis of the oligopolies competition market. In this particular model, the leader represents the OEM and the follower is the customer, where the OEM’s goal is to find a certain price structure to maximize his profit and consequently influence the buyer’s decision. Through this adaptation, the strategies and payoffs of players are defined. The robustness of the model is due to incorporating elements of the economic theory (consumer’s surplus, producer’s surplus, consumer’s reservation price, choice under uncertainty, maximum profit and contingent consumption plan) and elements of the reliability theory (probability of failure and non-repairable systems). Additionally, a numerical example and a sensitivity analysis of parameters are presented to highlight the model. Finally, this research systematizes the steps of Stackelberg game under the modeling of extended warranty (EW) as well.

Normative Utility Models for Pareto Scalar Equilibria in n-Person, Semi-Cooperative Games in Strategic Form

Semi-cooperative games in strategic form are considered in which either a negotiation among the n players determines their actions or else an arbitrator specifies them. Methods are presented for selecting such action profiles by using multiple-objective optimization techniques. In particular, a scalar equilibrium (SE) is an action profile for the n players that maximize a utility function over the acceptable joint actions. Thus the selection of “solutions” to the game involves the selection of an acceptable utility function. In a greedy SE, the goal is to assign individual actions giving each player the largest payoff jointly possible. In a compromise SE, the goal is to make individual player payoffs equitable, while a satisficing SE achieves a target payoff level while weighting each player for possible additional payoff. These SEs are formally defined and shown to be Pareto optimal over the acceptable joint actions of the players. The advantage of these SEs is that they involve only pure strategies that are easily computed. Examples are given, including some well-known coordination games, and the worst-case time complexity for obtaining these SEs is shown to be linear in the number of individual payoffs in the payoff matrix. Finally, the SEs of this paper are checked against some standard game-theoretic bargaining axioms.

Asynchronous updates can promote the evolution of cooperation on multiplex networks

We study the importance to the frequency of cooperation of the choice of updating strategies in a game played asynchronously or synchronously across layers in a multiplex network. Updating asynchronously in the public goods game leads to higher frequencies of cooperation compared to synchronous updates. How large this effect is depends on the sensitivity of the game dynamics to changes in the number of cooperators surrounding a player, with the largest effect observed when players payoffs are small. The discovery of this effect enhances understanding of cooperation on multiplex networks, and demonstrates a new way to maintain cooperation in these systems.

Price of anarchy for graph coloring games with concave payoff

We study the price of anarchy in graph coloring games (a subclass of polymatrix common-payoff games). Players are vertices of an undirected graph, and the strategies for each player are the colors $\left\{ {1, \ldots ,k} \right\}$ . A tight bound of $\frac{k}{k-1}$ is known (Hoefer 2007, Kun et al. 2013), if each player's payoff is the number of neighbors with different color than herself.In our generalization, payoff is computed by determining the distance of the player's color to the color of each neighbor, applying a concave function $f$ to each distance, and then summing up the resulting values. This is motivated, e. g., by spectrum sharing, and includes the payoff functions suggested by Kun et al. (2013) for future work as special cases.Denote $f^*$ the maximum value that $f$ attains on $\left\{ {0, \ldots ,k - 1} \right\}$ . We prove an upper bound of $2$ on the price of anarchy if $f$ is non-decreasing or assumes $f^*$ somewhere in $\left\{ {0, \ldots ,{\frac{k}{2}}} \right\}$ . Matching lower bounds are given for the monotone case and if $f^*$ is assumed in $\frac{k}{2}$ for even $k$ . For general concave $f$ , we prove an upper bound of $3$ . We use a new technique that works by an appropriate splitting $\lambda = \lambda_1 + \ldots + \lambda_k$ of the bound $\lambda$ we are proving.

Fairness Ideals in Distribution Channels

The authors analytically and experimentally evaluate how firms make decisions in a two-stage dyadic channel, in which firms decide on investments in the first stage and then on prices in the second stage. They find that firms’ behavior differs significantly from the predictions of the standard economic model and is consistent with the existence of fairness concerns. Using a quantal response equilibrium model, in which both manufacturer and retailer make noisy best responses, the authors show that fairness significantly affects channel pricing decisions. In addition, they investigate what affects the perceptions of fairness. More specifically, they analyze whether the notion of fairness is influenced by social norms of strict equality, by endogenous investments and contributions that are affected by players’ decisions, or by the exogenous game structure. To do so, the authors compare four principles of distributive fairness: strict egalitarianism; liberal egalitarianism; libertarianism; and a sequence-aligned ideal, which is studied for the first time in the literature. Surprisingly, the exogenous game structure reflected by the new ideal, whereby the sequence of moving determines the equitable payoff for players, significantly outperforms other fairness ideals, suggesting that equity in distribution channels can arise even in contests in which channel members have fairly different payoffs.

Take the Money and Run: Psychopathic Behavior in the Trust Game.

We study the association among different sources of individual differences such as personality, cognitive ability and risk attitudes with trust and reciprocate behavior in an incentivized experimental binary trust game in a sample of 220 (138 females) undergraduate students. The game involves two players, player 1 (P1) and player 2 (P2). In the first stage, P1 decides whether to trust and let P2 decide, or to secure an egalitarian payoff for both players. If P1 trusts P2, the latter can choose between a symmetric payoff that is double than the secure alternative discarded by P1, and an asymmetric payoff in which P2 earns more than in any other case but makes P1 worse off. Before the main experiment, we obtained participants’ scores for Reasoning (AR), risk attitudes, basic personality characteristics, and specific traits such as psychopathy and impulsivity. During the main experiment, we measured Heart Rate (HR) and ElectroDermal Activity (EDA) variation to account for emotional arousal caused by the decision and feedback processes. Our main findings indicate that, on one hand, P1 trust behavior associates to positive emotionality and, specifically, to the extraversion’s warmth facet. In addition, the impulsivity facet of positive urgency also favors trust behavior. No relation to trusting behavior was found for either other major personality aspects or risk attitudes. The physiological results show that participants scoring high in psychopathy exhibit increased EDA and reduced evoked HR deceleration at the moment in which they are asked to decide whether or not to trust. Regarding P2, we find that AR ability and mainly low disagreeable disinhibition favor reciprocal behavior. Specifically, lack of reciprocity significantly relates with a psychopathic, highly disinhibited and impulsive personality. Thus, the present study suggests that personality characteristics would play a significant role in different behaviors underlying cooperation, with extraversion/positive emotionality being more relevant for initiating cooperation, and low disagreeable disinhibition for maintaining it.

All-Pay Contests with Performance Spillovers

This paper generalizes the results of Siegel (2009, 2010) to accommodate performance spillovers. More precisely, we show that, if for any player, spillover from other players' performance is independent of his own performance, and if the spillover enters any player's payoff in an additively separable form, then an all-pay contest with spillovers has a unique Nash equilibrium. Moreover, we construct the equilibrium payoffs and strategies.

Estimation of games with ordered actions: An application to chain-store entry

We study the estimation of static games where players are allowed to have ordered actions, such as the number of stores to enter into a market. Assuming that payoff functions satisfy general shape restrictions, we show that equilibrium of the game implies a covariance restriction between each player's action and a component of the player's payoff function that we call the strategic index. The strategic index captures the direction of strategic interaction (i.e., patterns of substitutability or complementarity) as well as the relative effects of opponents' decisions on players' payoffs. The covariance restriction we derive is robust to the presence of multiple equilibria, and provides a basis for identification and estimation of the strategic index. We introduce an econometric method for inference in our model that exploits the information in moment inequalities in a computationally simple way. We analyze its properties through Monte Carlo experiments and then apply our approach to study entry behavior by chain stores where there is both an intensive margin of entry (how many stores to open in a market) as well as the usual extensive margin of entry (whether to enter a market or not). Using data from retail pharmacies we find evidence of asymmetries in strategic effects among firms in the industry that has implications for merger policy. We also find that business stealing effects are less pronounced in larger markets, which helps explain the large positive correlation in entry behavior observed in the data. Static games multiple equilibria partial identification conditional moment inequalities entry decisions C01 C14 C57

Agglomeration, Segregation, and Social Welfare in Group Formation Games

We consider a non cooperative game in which a continuum of heterogeneous individuals partition themselves into groups. A player's payoff depends on the group she chooses and the set of players who choose the same group as her.In the case of anonymous group externalities, we show that free mobility equilibria are socially optimal when group externalities vary logarithmically with community size. When they increase less (more) than logarithmically, the equilibrium partition exhibits excessive agglomeration (excessive fragmentation). In the case of nonanonymous group externalities, free mobility affects the size, but also the composition of groups. We characterize conditions under which free mobility equilibria are excessively or insufficiently segregated.When applied to local public goods economies, these results provide insights on the social welfare effect of free mobility as a function of the local public good technology, the income distribution, and the tax scheme.

Nonlocal correlations: Fair and unfair strategies in Bayesian games

Interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform classical equilibrium strategies in common interest Bayesian games and also in conflicting interest games. However, classical equilibrium strategies can be of two types, fair and unfair. Whereas in fair equilibrium payoffs of different players are same, in unfair case they differ. Advantage of nonlocal correlation has been demonstrated over fair strategies. In this work we show that quantum strategies can outperform even the unfair classical equilibrium strategies. For this purpose we consider a class of two players games which as a special case includes the conflicting game proposed in [Phys. Rev. Lett. 114, 020401 (2015)]. These games can have both fair and unfair classical equilibria and also can have only unfair ones. We provide a simple analytic characterization of the nonlocal correlations that are advantageous over the classical equilibrium strategies in these games.

Estimation of games with ordered actions: An application to chain‐store entry

We study the estimation of static games where players are allowed to have ordered actions, such as the number of stores to enter into a market. Assuming that payoff functions satisfy general shape restrictions, we show that equilibrium of the game implies a covariance restriction between each player's action and a component of the player's payoff function that we call the strategic index. The strategic index captures the direction of strategic interaction (i.e., patterns of substitutability or complementarity) as well as the relative effects of opponents' decisions on players' payoffs. The covariance restriction we derive is robust to the presence of multiple equilibria, and provides a basis for identification and estimation of the strategic index. We introduce an econometric method for inference in our model that exploits the information in moment inequalities in a computationally simple way. We analyze its properties through Monte Carlo experiments and then apply our approach to study entry behavior by chain stores where there is both an intensive margin of entry (how many stores to open in a market) as well as the usual extensive margin of entry (whether to enter a market or not). Using data from retail pharmacies we find evidence of asymmetries in strategic effects among firms in the industry that has implications for merger policy. We also find that business stealing effects are less pronounced in larger markets, which helps explain the large positive correlation in entry behavior observed in the data. Static games multiple equilibria partial identification conditional moment inequalities entry decisions C01 C14 C57

Voting in collective best-choice problem with complete information

This paper considers a noncooperative m-player best-choice game with complete information about the quality parameters of incoming candidates. Collective decision-making is based on voting. The optimal threshold strategies and payoffs of the players are found depending on the voting threshold. The results of numerical simulation are presented.

Stochastic cooperative advertising in a manufacturer\u2013retailer decentralized supply channel

This work considers cooperative advertising in a manufacturer–retailer supply chain. While the manufacturer is the Stackelberg leader, the retailer is the follower. Using Sethi model it models the dynamic effect of the manufacturer and retailer’s advertising efforts on sale. It uses optimal control technique and stochastic differential game theory to obtain the players’ advertising strategies and the long-run value of the awareness share. Further, it models the relationship between the payoffs of both players and the awareness share. The work shows that with the provision of subsidy the retail advertising effort increases while the manufacturer’s advertising effort reduces. It further shows that the total channel payoff is higher for subsidised retail advertising. However, the subsidy can only be possible if the rate of growth of the manufacturer’s payoff is twice higher than that of the retailer.

Game theoretic hypergraph matching for multi-source image correspondences

In this paper, we develop a game theoretic hypergraph matching framework which enables refining feature correspondences of multi-source images. For images obtained from different sources, we commence by characterizing game strategies in terms of coarse correspondences based on feature similarities. In this scenario, mismatches tend to occur because one feature descriptor may exhibit certain ambiguity in characterizing feature similarities for multi-source images. To address this shortcoming, we develop payoffs for independent game players in terms of higher order strategy similarities, and identify strategies which extinguish in an evolutionary game for achieving maximum average payoff. To render a convenient computational framework, we establish an association uniform hypergraph, referred to as the game hypergraph, with each vertex representing a strategy and each uniform hyperedge characterizing a payoff for independent players. We then exploit the Baum–Eagon scheme for computing the maximum average game payoff for Nash equilibrium within the association hypergraph. Our method is invariant to scene scale variation because of the higher order structures characterized by the strategy similarities. Furthermore, our method is computationally more efficient than existing hypergraph matching methods because of coarse correspondences. Experimental results show the effectiveness of our method for refining multi-source feature correspondences.

Bilateral Delegation in Duopoly Wage and Employment Bargaining

We study bilateral delegation in wage and employment bargaining between firms and unions in a Cournot duopoly. Incentive delegation creates frictions for each party between its objectives of within‐firm rent extraction and market/job stealing from the rival firm. The net effect is restraint in production, resulting in a larger bargaining pie. But each player's payoff will be inversely related to his bargaining power. We also show that if players are given a choice to delegate, they will not resort to delegation when their bargaining power is sufficiently high. This is in contrast to the scenarios commonly assumed in many models. Copyright © 2016 John Wiley & Sons, Ltd.

Extension of a spatial evolutionary coordination game with neutral options

The multiagent evolutionary games on a lattice are equivalent to a kinetic Ising model if the uniform pair interactions are defined by a two-strategy coordination game and the logit rule controls the strategy updates. Now we extend this model by allowing the players to use additional neutral strategies that provide zero payoffs for both players if one of them selects one of the neutral strategies. In the resulting n-strategy evolutionary games the analytical methods and numerical simulations indicate continuous order-disorder phase transitions when increasing the noise level if n does not exceed a threshold value. For larger n the system exhibits a first order phase transition at a critical noise level decreasing asymptotically as 2/ln(n).

An Efficient Approach for Stimulating Cooperation among Nodes in Wireless Sensor Networks

A Wireless Sensor Network (WSN), characterized as being self-organizing and multihop, consists of a large number of low-power and low-cost nodes. The cooperation among nodes is the foundation for WSNs to achieve the desired functionalities, such as the delivery or forwarding of packets. However, due to the limited resources such as energy, computational availability, and communication capabilities, there may exist some selfish nodes that refuse to cooperate with others. If the critical masses of nodes do not cooperate in the network, the network would not be able to operate to achieve its functional requirements. To resolve the problem above, we introduce a Win-Stay, Lose-Likely-Shift (WSLLS) approach into a Prisoner's Dilemma (PD) game framework, and it applies a utility-based function, which is a linear combination of one player's payoff and its neighbors' in a game, to evaluate a player's (i.e., node) performance for a game. Experimental results demonstrate that our approach performs well in stimulating cooperation in different settings under a certain condition with limited information, regardless of the static topologies types of WSNs, initial proportion of cooperation, and the average number of neighbors.

Leading the Game, Losing the Competition: Identifying Leaders and Followers in a Repeated Game.

We explore a new method for identifying leaders and followers, LF, in repeated games by analyzing an experimental, repeated (50 rounds) game where Row player shifts the payoff between small and large values–a type of “investor” and Column player determines who gets the payoff–a type of “manager”. We found that i) the Investor (Row) most often is a leading player and the manager (Column) a follower. The longer the Investor leads the game, the higher is both player’s payoff. Surprisingly however, it is always the Manager that achieves the largest payoff. ii) The game has an efficient cooperative strategy where the players alternate in receiving a high payoff, but the players never identify, or accept, that strategy. iii) Under the assumption that the information used by the players is closely associated with the leader- follower sequence, and that information is available before the player’s decisions are made, the players switched LF- strategy primarily as a function of information on the Investor’s investment and moves and secondly as a function of the Manager’s payoff.