Selfish Players Research Articles

Rewards and the private provision of public goods on dynamic networks

We study an evolutionary model of a public good game with rewards played on a network. Giving rewards to contributors transforms the game but gives rise to a second-order dilemma. By allowing for coevolution of strategies and network structure, the evolutionary dynamics operate on both structure and strategy. Players learn with whom to interact and how to act and can overcome the second-order dilemma. More specifically, the network represents social distance which changes as players interact. Through the change in social distance, players learn with whom to interact, which we model using reinforcement dynamics. We find that, for certain parameter constellations, a social institution, prescribing prosocial behavior and thus solving the second-order dilemma, can emerge from a population of selfish players. Due to the dynamic structure of the network, the institution has an endogenous punishment mechanism ensuring that defectors will be excluded from the benefits of the institution and the public good will be supplied efficiently.

Play it Again: Partner Choice, Reputation Building and Learning in Restarting, Finitely-Repeated Dilemma Games

Previous research has shown that opportunities for two-sided partner choice in finitely repeated social dilemma games can promote cooperation through a combination of sorting and opportunistic signaling, with late period defections by selfish players causing an end-game decline. How such experience would affect play of subsequent finitely-repeated games remains unclear. In each of six treatments that vary the cooperation premium and the informational basis for reputation formation, we let sets of subjects play sequences of finitely-repeated voluntary contribution games to study the competing forces of (a) learning about the benefits of reputation, and (b) learning about backward unraveling. We find, inter alia, that with a high cooperation premium and good information, investment in reputation grows across sets of finitely-repeated games.

Coding-Aware Peer-to-Peer Data Repair in Multi-Rate Wireless Networks: A Game Theoretic Analysis

Recent research shows that in wireless wide area networks (WWANs), users who subscribe to multicast traffic from WWAN can exchange network-coded packets with one another via their secondary radio interfaces such as Wi-Fi in order to efficiently recover lost packets from the WWAN. Different from existing works which assume users are cooperative, in this work, we model the users as selfish players in the network-coding based peer-to-peer packet repairing game. To stimulate the users' cooperation, we introduce a payment-based incentive mechanism in the packet repairing game. The utility function of a user/player is also formulated to reflect both the number of useful packets and the available resource. Through analysis of the packet repairing game, we show that the optimal strategy for a user can be derived only with its local information. The impact of the pricing rules and the convergence conditions of the packet repairing game is also analyzed. We show theoretically as well as by simulation that under proper conditions, the packet repairing game can converge to the best case where each user can acquire all of its missing packets. Via computer simulations, we also show that with the proposed selection criteria, the packet repairing game is both effective and efficient: not only can the utilities of the players be greatly improved, but also the convergence time of the game and the utility gain of the players are comparable to those of the ideal case where every user is always willing to forward packets to others.

Selfish bin packing with cardinality constraints

Bin packing with cardinality constraints is a variant of bin packing. In this problem, items with sizes of at most 1 are to be partitioned (or packed) into subsets called bins, such that the total size of items packed into a bin would not exceed 1, and each bin would contain at most k items, for a given integer parameter k>1.We consider a class of games resulting from this problem by seeing the items as selfish players, trying to be packed into a (valid) bin where the total size of items is maximized. Such games always admit pure Nash equilibria. We analyze the Price of Anarchy (PoA) of such games, defined as the asymptotic worst case ratio between the maximum number of bins in a pure Nash equilibrium (NE), and the minimum number of bins in any valid solution, that is, the number of bins in a socially optimal solution. We provide a complete analysis of the PoA as a function of k; we prove that for k=2, any NE is an optimal solution, for k⩾4, the PoA is exactly 2−1k, and for k=3, the PoA is exactly 117.

An Improved Fitness Evaluation Mechanism with Memory in Spatial Prisoner's Dilemma Game on Regular Lattices

To deeply understand the emergence of cooperation in natural, social and economical systems, we present an improved fitness evaluation mechanism with memory in spatial prisoner's dilemma game on regular lattices. In our model, the individual fitness is not only determined by the payoff in the current game round, but also by the payoffs in previous round bins. A tunable parameter, termed as the memory strength (μ), which lies between 0 and 1, is introduced into the model to regulate the ratio of payoffs of current and previous game rounds in the individual fitness calculation. When μ = 0, our model is reduced to the standard prisoner's dilemma game; while μ = 1 represents the case in which the payoff is totally determined by the initial strategies and thus it is far from the realistic ones. Extensive numerical simulations indicate that the memory effect can substantially promote the evolution of cooperation. For μ < 1, the stronger the memory effect, the higher the cooperation level, but μ = 1 leads to a pathological state of cooperation, but can partially enhance the cooperation in the very large temptation parameter. The current results are of great significance for us to account for the role of memory effect during the evolution of cooperation among selfish players.

A Control Method of Dynamic Selfish Routing Based on a State-Dependent Tax

SUMMARY A selfish routing game is a simple model of selfish behaviors in networks. It is called that Braess’s paradox occurs in the selfish routing game if an equilibrium flow achieved by players’ selfish behaviors is not the optimal minimum latency flow. In order to make the minimum latency flow a Nash equilibrium, a marginal cost tax has been proposed. Braess graphs have also been proposed to discuss Braess’s paradox. In a large population of selfish players, conflicts between purposes of each player and the population causes social dilemmas. In game theory, to resolve the social dilemmas, a capitation tax and/or a subsidy has been introduced, and players’ dynamical behaviors have been formulated by replicator dynamics. In this paper, we formulate replicator dynamics in the Braess graphs and investigate stability of the minimum latency flow with and without the marginal cost tax. An additional latency caused by the marginal cost tax is also shown. To resolve the problem of the additional latency, we extend the capitation tax and the subsidy to a state-dependent tax and apply it to the stabilization problem of the minimum latency flow.

BNE-based concurrent transmission considering channel quality and its PSO searching strategy in Ad Hoc networks

The paper proposes a decentralized concurrent transmission strategy in shared channels based on an incomplete information game in Ad Hoc networks. Based on the nodal channel quality, the game can work out a channel gain threshold, which decides the candidates for taking part in the concurrent transmission. The utility formula is made for maximizing the overall throughput based on channel quality variation. For an achievable Bayesian Nash equilibrium (BNE) solution, this paper further prices the selfish players in utility functions for attempting to improve the channel gain one-sidedly. Accordingly, this game allows each node to distributedly decide whether to transmit concurrently with others depending on the Nash equilibrium (NE). Besides, to make the proposed game practical, this paper next presents an efficient particle swarm optimization (PSO) model to fasten the otherwise very slow convergence procedure due to the large computational complexity. Numerical results show the proposed approach is feasible to increase concurrent transmission opportunities for active nodes and the convergence can be swiftly obtained with a few of iteration times by the proposed PSO algorithm.

Sorting and sustaining cooperation

This paper looks at cooperation in teams where some people are selfish and others are conditional cooperators, and where lay-offs will occur at a fixed future date. I show that the best way to sustain cooperation prior to the lay-offs is often in a sorting equilibrium, where conditional cooperators can identify and then work with one another. Changes to parameters that would seem to make cooperation more attractive, such as an increase in the discount factor or the fraction of conditional cooperators, can reduce equilibrium cooperation if they decrease a selfish player's incentive to sort. Copyright 2013 Oxford University Press 2012 All rights reserved, Oxford University Press.

Utility‐driven construction of balanced data routing trees in wireless sensor networks

ABSTRACTIn wireless sensor networks, achieving load balancing in an energy‐efficient manner to improve the network lifetime as much as possible is still a challenging problem because in such networks, the only energy resource for sensor nodes is their battery supplies. This paper proposes a game theoretical‐based solution in the form of a distributed algorithm for constructing load‐balanced routing trees in wireless sensor networks. In our algorithm, load balancing is realized by adjusting the number of children among parents as much as possible, where child adjustment is considered as a game between the parents and child nodes; parents are considered as cooperative players, and children are considered as selfish players. The gained utility by each node is determined by means of some utility functions defined per role, which themselves determine the behavior of nodes in each role. When the game is over, each node gains the maximum benefit on the basis of its utility function, and the balanced tree is constructed. The proposed method provides additional benefits when in‐network aggregation is applied. Analytical and simulation results are provided, demonstrating that our proposed algorithm outperform two recently proposed benchmarking algorithms [1, 2], in terms of time complexity and communication overhead required for constructing the load‐balanced routing trees. Copyright © 2012 John Wiley &amp; Sons, Ltd.

A note on a selfish bin packing problem

In this paper, we consider a selfish bin packing problem, where each item is a selfish player and wants to minimize its cost. In our new model, if there are k items packed in the same bin, then each item pays a cost 1/k, where k ? 1. First we find a Nash Equilibrium (NE) in time O(n log n) within a social cost at most 1.69103OPT + 3, where OPT is the social cost of an optimal packing; where n is the number of items or players; then we give tight bounds for the worst NE on the social cost; finally we show that any feasible packing can be converged to a Nash Equilibrium in O(n 2) steps without increasing the social cost.

Study on Overlapping Community Structure

Discovery and classification of overlap nodes in communities is an important topic in data mining. In this paper, a new method is proposed, it is based on fuzzy bargaining sets. To uncover overlap nodes, we assume that each node is a selfish player who selects communities to join by participation level base on her own utility measurement. We allow each player to select multiple communities, which naturally captures the concept of “overlapping communities”. We conduct experiments on this method, and the results show that our algorithm is effective in discovering overlapping communities, the value in practice and academic study is demonstrated.

Repeated rational secret sharing, revisited

Rational Secret Sharing Scheme (RSSS) disposes the dilemma that several selfish players come together and willingly pool their shares to reconstruct a secret without a compulsory execution measure, while cooperation is not a strict optimisation. This paper introduces four punishment strategies and expands the perfect conclusions in infinitely repeated RSSS to show that cooperation will recur by means of some strategies. For finitely repeated RSSS, this paper verifies that there is no way for players to cooperate under perfect and complete information for backward induction. To overcome this difficulty, this paper relaxes conditions such as the types of players and the randomised strategies. It is proved that, given the different types and incomplete information, players will insist on cooperation in finitely repeated RSSS. In addition, we discuss repeated games in an extensive form and propose a 2-out-of-2 RSSS.

A distributed resource management model for Virtual Private Networks: Tit-for-Tat strategies

In this paper, we address the autonomic resource management problem for Virtual Private Networks (VPNs) in the presence of stochastic and selfish VPN operators. Resource management is one of the most important problems that faces Internet Service Providers. In the literature, the Autonomic Service Architecture is proposed to provide a resource management model that allows systems to manage themselves and aiming to utilize optimally the unused resources. Unfortunately, this model suffers from two major limitations. First, unused resources from underloaded VPNs ( lenders) are utilized over the overloaded ones ( borrowers) without considering the unexpected changes of the VPNs’ state, which may often happen in the case of multimedia transmissions. This may affect negatively the Quality-of-Service (QoS) of the lenders while improving the QoS of the borrowers. Second, underloaded VPNs’ operators might behave selfishly and refuse to lend their unused (spare) resources to other overloaded VPNs. To overcome these limitations, we propose a distributed autonomic resource management, which is modeled as a repeated non-cooperative game with stochastic and selfish players. The classical Tit-for-Tat strategy is modified to cope with VPN operators who are not always able to lend some resources to others. Four different strategies are derived from Tit-for-Tat to motivate VPN operators to lend their resources to others. As far as we know, our work is among the first efforts that uses repeated non-cooperative game theory to motivate selfish participants to cooperate and to distinguish between stochastic and purely selfish VPNs’ operators. In our setting, this results in cooperative sharing of unused resources among VPNs. Simulation results show that Tit-for-Tat strategy leads to deadlocks, while our strategies assure good gains to cooperative VPN operators and punish the selfish ones.

Nonconvex Games with Side Constraints

This paper develops an optimization-based theory for the existence and uniqueness of equilibria of a noncooperative game wherein the selfish players' optimization problems are nonconvex and there are side constraints and an associated price clearance to be satisfied by the equilibria. A new concept of equilibrium for such a nonconvex game, which we term a “quasi-Nash equilibrium” (QNE), is introduced as a solution of the variational inequality (VI) obtained by aggregating the first-order optimality conditions of the players' problems while retaining the convex constraints (if any) in the defining set of the VI. Under a second-order sufficiency condition from nonlinear programming, a QNE becomes a local Nash equilibrium of the game. Uniqueness of a QNE is established using a degree-theoretic proof. Under a key boundedness property of the Karush-Kuhn-Tucker multipliers of the nonconvex constraints and the positive definiteness of the Hessians of the players' Lagrangian functions, we establish the single-valuedness of the players' best-response maps, from which the existence of a Nash equilibrium (NE) of the nonconvex game follows. We also present a distributed algorithm for computing an NE of such a game and provide a matrix-theoretic condition for the convergence of the algorithm. An application is presented that pertains to a special multi-leader-follower game wherein the nonconvexity is due to the followers' equilibrium conditions in the leaders' optimization problems. Another application to a cognitive radio paradigm in a signal processing game is described in detail in [G. Scutari and J.S. Pang, IEEE Trans. Inform. Theory, submitted; J.S. Pang and G. Scutari, Joint IEEE Trans. Signal Process, submitted].

Routing (un-) splittable flow in games with player-specific affine latency functions

In this work we study weighted network congestion games with player-specific latency functions where selfish players wish to route their traffic through a shared network. We consider both the case of splittable and unsplittable traffic. Our main findings are as follows. For routing games on parallel links with linear latency functions, we introduce two new potential functions for unsplittable and for splittable traffic, respectively. We use these functions to derive results on the convergence to pure Nash equilibria and the computation of equilibria. For several generalizations of these routing games, we show that such potential functions do not exist. We prove tight upper and lower bounds on the price of anarchy for games with polynomial latency functions. All our results on the price of anarchy translate to general congestion games.

How Bad Are Selfish Investments in Network Security?

We study a network security game where strategic players choose their investments in security. Since a player's investment can reduce the propagation of computer viruses, a key feature of the game is the positive externality exerted by the investment. With selfish players, unfortunately, the overall network security can be far from optimum. The contributions of this paper are as follows. 1) We first characterize the price of anarchy (POA) in the strategic-form game under an “Effective-investment” model and a “Bad-traffic” model, and give insight on how the POA depends on individual players' cost functions and their mutual influence. We also introduce the concept of “weighted POA” to bound the region of payoff vectors. 2) In a repeated game, players have more incentive to cooperate for their long term interests. We consider the socially best outcome that can be supported by the repeated game, as compared to the social optimum. 3) Next, we compare the benefits of improving security technology and improving incentives, and show that improving technology alone may not offset the price of anarchy. 4) Finally, we characterize the performance of correlated equilibrium (CE). Although the paper focuses on network security, many results are generally applicable to games with positive externalities .

Selfishness, fraternity, and other-regarding preference in spatial evolutionary games

Spatial evolutionary games are studied with myopic players whose payoff interest, as a personal character, is tuned from selfishness to other-regarding preference via fraternity. The players are located on a square lattice and collect income from symmetric two-person two-strategy (called cooperation and defection) games with their nearest neighbors. During the elementary steps of evolution a randomly chosen player modifies her strategy in order to maximize stochastically her utility function composed from her own and the co-players' income with weight factors 1−Q and Q. These models are studied within a wide range of payoff parameters using Monte Carlo simulations for noisy strategy updates and by spatial stability analysis in the low noise limit. For fraternal players (Q=1/2) the system evolves into ordered arrangements of strategies in the low noise limit in a way providing optimum payoff for the whole society. Dominance of defectors, representing the “tragedy of the commons”, is found within the regions of prisoner's dilemma and stag hunt game for selfish players (Q=0). Due to the symmetry in the effective utility function the system exhibits similar behavior even for Q=1 that can be interpreted as the “lovers' dilemma”.

Convergence to Equilibria in Distributed, Selfish Reallocation Processes with Weighted Tasks

We consider the problem of dynamically reallocating (or re-routing) m weighted tasks among a set of n uniform resources (one may think of the tasks as selfish players). We assume an arbitrary initial placement of tasks, and we study the performance of distributed, natural reallocation algorithms. We are interested in the time it takes the system to converge to an equilibrium (or get close to an equilibrium). Our main contributions are (i) a modification of the protocol in 2006 that yields faster convergence to equilibrium, together with a matching lower bound, and (ii) a non-trivial extension to weighted tasks.

Cooperation over finite horizons: A theory and experiments

This paper shows that the presence of different types of players – those who only care about their own material payoffs and those who reciprocate others' contributions – can explain the robust features of observed contribution patterns in public good contribution games, even without the presence of asymmetric information. We show what conditions on reciprocity are sufficient for a unique perfect equilibrium, in which contributions are decreasing. Under these conditions, selfish players have enough future benefits to induce subsequent contributions by reciprocal players, and this incentive diminishes as the end of the game approaches. The model explains the puzzling restart effect and is consistent with various other empirical findings. We also report the results of a series of experiments, using a probabilistic continuation design in which after each set of 10-period games, the group is restarted with low probability. We find specific support for the theory in our data, including that selfish players (identified exogenously) stop contributing earlier than reciprocal players, as directly implied by the model.

TWO-STEP "WIN-STAY, LOSE-SHIFT" AND LEARNING TO COOPERATE IN THE REPEATED PRISONER'S DILEMMA

The standard win-stay, lose-shift behavior strategy in the repeated Prisoner's Dilemma game prescribes the players that win and lose in a current game round to keep and to change, respectively, their current actions, in the next round. Winning and losing are understood as receiving one of two upper values and one of two lower values, respectively, among the four admissible values for the players' benefits. In particular, a player acting as a cooperator against cooperation wins and therefore is not allowed to switch to defection in the next round with a hope to gain more (provided his/her rival keeps cooperating). This constraint can be viewed as too strong for a selfish player. Here, we discuss a two-step win-stay, lose-shift behavior that differs from the traditional win-stay lose-shift one in understanding of winning and losing. A player wins if his/her benefit is no smaller that in the previous round, and loses otherwise. This pattern is in a sense more selfish; in particular, a switch from cooperation (against cooperation) to defection is not forbidden. Another confirmation of a more selfish character of the two-step win-stay, lose-shift behavior, compared to the standard win-stay, lose-shift one, is that the former does not bring two individuals playing the repeated Prisoner's Dilemma game to mutual cooperation. In this paper, our goal is to understand to what degree one can relax the two-step win-stay, lose-shift behavior in selfishness so as to reach mutual cooperation, anyway. We deal with two models of the repeated Prisoner's Dilemma game — a game of two individuals and a game in a group of players. In the game of two individuals, a relaxed two-step win-stay, lose-shift behavior assumes that the players use mixed strategies; here, relaxation is associated with patience. In the game in a group of players, relaxation is achieved through conformity, a tendency to join the majority. We show that even a small degree of conformity is enough to teach a two-step win-stay, lose-shift group to cooperate.