Selfish Players Research Articles

Effectiveness of the approval mechanism in a three-player common pool resource dilemma

Selfish players in common pool resources games (CPR) prevent to reach socially efficient outcomes. To solve this CPR dilemma, we investigate further the approval mechanism (AM) in a three-player CPR game. Adding a third player is useful to test the efficiency of approval rules, i.e. majority versus unanimity, in the second stage of the AM. We find that the AM mitigates over-exploitation in three player CPR games, and that unanimity performs better than majority. Nevertheless, with three players, the mechanism surprisingly works better in case of approval failure rather than approval success. However, most approvals are predicted.

Social Expectations are Primarily Rooted in Reciprocity: An Investigation of Fairness, Cooperation, and Trustworthiness.

Social expectations guide people's evaluations of others' behaviors, but the origins of these expectations remain unclear. It is traditionally thought that people's expectations depend on their past observations of others' behavior, and people harshly judge atypical behavior. Here, we considered that social expectations are also influenced by a drive for reciprocity, and people evaluate others' actions by reflecting on their own decisions. To compare these views, we performed four studies. Study 1 used an Ultimatum Game task where participants alternated Responder and Proposer roles. Modeling participants' expectations suggested they evaluated the fairness of received offers via comparisons to their own offers. Study 2 replicated these findings and showed that observing selfish behavior (lowball offers) only promoted acceptance of selfishness if observers started acting selfishly themselves. Study 3 generalized the findings, demonstrating that they also arise in the Public Goods Game, emerge cross-culturally, and apply to antisocial punishment whereby selfish players punish generosity. Finally, Study 4 introduced the Trust Game and showed that participants trusted players who reciprocated their behavior, even if it was selfish, as much as they trusted generous players. Overall, this research shows that social expectations and evaluations are rooted in drives for reciprocity. This carries theoretical implications, speaking to a parallel in the mechanisms driving both decision-making and social evaluations, along with practical importance for understanding and promoting cooperation.

Altruistic Hedonic Games

Hedonic games are coalition formation games in which players have preferences over the coalitions they can join. For a long time, all models of representing hedonic games were based upon selfish players only. Among the known ways of representing hedonic games compactly, we focus on friend-oriented hedonic games and propose a novel model for them that takes into account not only the players’ own preferences but also their friends’ preferences. Depending on the order in which players look at their own or their friends’ preferences, we distinguish three degrees of altruism: selfish-first, equal-treatment, and altruistic-treatment preferences. We study both the axiomatic properties of these games and the computational complexity of problems related to various common stability concepts.

Nash Social Welfare in Selfish and Online Load Balancing

In load-balancing problems there is a set of clients, each wishing to select a resource from a set of permissible ones to execute a certain task. Each resource has a latency function, which depends on its workload, and a client’s cost is the completion time of her chosen resource. Two fundamental variants of load-balancing problems are selfish load balancing (a.k.a. load-balancing games ), where clients are non-cooperative selfish players aimed at minimizing their own cost solely, and online load balancing , where clients appear online and have to be irrevocably assigned to a resource without any knowledge about future requests. We revisit both problems under the objective of minimizing the Nash Social Welfare , i.e., the geometric mean of the clients’ costs. To the best of our knowledge, despite being a celebrated welfare estimator in many social contexts, the Nash Social Welfare has not been considered so far as a benchmarking quality measure in load-balancing problems. We provide tight bounds on the price of anarchy of pure Nash equilibria and on the competitive ratio of the greedy algorithm under very general latency functions, including polynomial ones. For this particular class, we also prove that the greedy strategy is optimal, as it matches the performance of any possible online algorithm.

Many-to-one stable matching for taxi-sharing service with selfish players

In taxi-sharing, matching problems can be divided into two parts, i.e., passenger-to-taxi matches and passenger-to-passenger matches. Considering of the selfishness of passengers and taxi drivers, attention needs to be devoted to their preferences over matching partners. In this paper, the concept of the scheme is introduced as a medium to formulate the preferences of passengers and taxi drivers. A stable matching framework is first designed to model the matching problem of taxi-sharing service with peer effect. A branch-and-price algorithm is tailored to solve the many-to-one stable matching problem. Dalian taxi data are used to assess the performance of the proposed model and algorithm. The results indicate that the variable discount strategy is a useful tool to balance the demand and supply. The matching rate of taxis increases by an average of 5.39% compared with the fixed discount strategy. Furthermore, when the taxi-sharing reaches a high level of participation, the benefit received from expanding the service space of taxis from a 3-min drive to a 10-min drive is limited. However, a relaxed preference rule could increase the matching rate of passengers by 25.6%. When the passengers’ preferences over co-riders are not considered as the traditional preference rule, the waiting time of passengers increases by 77.1%.

Game-Theoretic Power and Rate Control in IEEE 802.11p Wireless Networks

Optimization of the transmission power and rate allocation is a significant problem in wireless networks with mobile nodes. Due to mobility, the vehicles establishing wireless networks may exhibit severe fluctuations of their link quality, affecting their connection reliability and throughput. In Vehicular Ad-hoc Networks (VANETS), the IEEE 802.11p standard provides a practical metric for the Packet Reception Ratio (PRR), which is related with the transmission power and rate. Finding a global strategy for optimizing PRR for all mobile nodes can be treated as a potential game where each vehicle is considered as a selfish player, aiming to maximise its transmission reliability while rate constraints are satisfied. To this end, we propose a game-theoretic approach that converges to a Nash equilibrium. The main contributions of this work include: (i) identification of the best case equilibrium, for two cases of interference: diminished or kept stable, and (ii) verification of the equilibrium optimality, by showing that the value of stability is 1. Moreover, numerical results exhibiting the ease of the utility function calculation are provided, especially after an SINR level, whereby the utility function is concave and can be solved efficiently in polynomial time.

Payoff landscapes and the robustness of selfish optimization in iterated games.

In iterated games, a player can unilaterally exert influence over the outcome through a careful choice of strategy. A powerful class of such "payoff control" strategies was discovered by Press and Dyson (2012). Their so-called "zero-determinant" (ZD) strategies allow a player to unilaterally enforce a linear relationship between both players' payoffs. It was subsequently shown by Chen and Zinger (2014) that when the slope of this linear relationship is positive, ZD strategies are robustly effective against a selfishly optimizing co-player, in that all adapting paths of the selfish player lead to the maximal payoffs for both players (at least when there are certain restrictions on the game parameters). In this paper, we investigate the efficacy of selfish learning against a fixed player in more general settings, for both ZD and non-ZD strategies. We first prove that in any symmetric 2[Formula: see text]2 game, the selfish player's final strategy must be of a certain form and cannot be fully stochastic. We then show that there are prisoner's dilemma interactions for which selfish optimization does not always lead to maximal payoffs against fixed ZD strategies with positive slope. We give examples of selfish adapting paths that lead to locally but not globally optimal payoffs, undermining the robustness of payoff control strategies. For non-ZD strategies, these pathologies arise regardless of the original restrictions on the game parameters. Our results illuminate the difficulty of implementing robust payoff control and selfish optimization, even in the simplest context of playing against a fixed strategy.

A Framework for Studying Decentralized Bayesian Learning with Strategic Agents

We study the problem of Bayesian learning in a dynamical system involving strategic agents with asymmetric information. In a series of seminal papers in the literature, this problem has been investigated under a simplifying model where selfish players appear sequentially and act once in the game. It has been shown that there exist information cascades where users discard their private information and mimic the action of their predecessor. In this paper, we provide a framework for studying Bayesian learning dynamics in a more general setting than the one just described. In particular, our model incorporates cases where players can act repeatedly and there is strategic interaction in that each agent’s payoff may also depend on other players’ actions. The proposed framework hinges on a sequential decomposition methodology for finding structured perfect Bayesian equilibria of a general class of dynamic games with asymmetric information. Using this methodology, we study a specific dynamic learning model where players make decisions about public investment based on their estimates of everyone’s states. We characterize a set of informational cascades for this problem where learning stops for the team as a whole. Moreover, we show that such cascades occur almost surely.

Additively Separable Hedonic Games with Social Context

In hedonic games, coalitions are created as a result of the strategic interaction of independent players. In particular, in additively separable hedonic games, every player has valuations for all other ones, and the utility for belonging to a coalition is given by the sum of the valuations for all other players belonging to it. So far, non-cooperative hedonic games have been considered in the literature only with respect to totally selfish players. Starting from the fundamental class of additively separable hedonic games, we define and study a new model in which, given a social graph, players also care about the happiness of their friends: we call this class of games social context additively separable hedonic games (SCASHGs). We focus on the fundamental stability notion of Nash equilibrium, and study the existence, convergence and performance of stable outcomes (with respect to the classical notions of price of anarchy and price of stability) in SCASHGs. In particular, we show that SCASHGs are potential games, and therefore Nash equilibria always exist and can be reached after a sequence of Nash moves of the players. Finally, we provide tight or asymptotically tight bounds on the price of anarchy and the price of stability of SCASHGs.

Local reputation, local selection, and the leading eight norms

Humans are capable of solving cooperation problems following social norms. Social norms dictate appropriate behaviour and judgement on others in response to their previous actions and reputation. Recently, the so-called leading eight norms have been identified from many potential social norms that can sustain cooperation through a reputation-based indirect reciprocity mechanism. Despite indirect reciprocity being claimed to extend direct reciprocity in larger populations where direct experiences cannot be accumulated, the success of social norms have been analysed in models with global information and evolution. This study is the first to analyse the leading eight norms with local information and evolution. We find that the leading eight are robust against selfish players within most scenarios and can maintain a high level of cooperation also with local information and evolution. In fact, local evolution sustains cooperation under a wider set of conditions than global evolution, while local reputation does not hinder cooperation compared to global reputation. Four of the leading eight norms that do not reward justified defection offer better chances for cooperation with quick evolution, reputation with noise, larger networks, and when unconditional defectors enter the population.

Game-Theory-Based Clustering Scheme for Energy Balancing in Underwater Acoustic Sensor Networks

The underwater acoustic sensor network (UASN) is a specific deployment of Internet-of-Things (IoT) technology in the underwater environment, since energy constraints limit the lifetime of UASNs, effectively balancing the energy consumption of acoustic sensor nodes in UASNs is important to maximize the amount of information collected and to prolong the network lifetime. Node clustering is widely regarded as one of the most important energy-efficient schemes for UASNs. However, most existing clustering schemes focus on the cooperation-based election of cluster headers (CHs) in a centralized manner. Due to the limited energy capacity, acoustic sensor nodes are designed to save their own energy, hindering the realization of such cooperation. To address this issue in this article, game theory is applied to UASNs to balance network energy consumption and model acoustic sensor nodes as rational and selfish players. Specifically, a game-theory-based clustering (GTC) scheme for UASNs is developed. In the CH election phase, each node makes a decision in pursuit of a greater payoff based on the Nash equilibrium. An incentive mechanism is invented to induce nodes to make more beneficial collective decisions and plays a role in the CH rotation to effectively balance the energy consumption. Meanwhile, the network area is divided into nonuniform sectors to ensure the energy consumption of the CH is more evenly distributed. Simulation results show that the proposed GTC scheme can effectively balance network energy consumption and extend the network lifetime.

Evolutionary Stability of Preferences: Altruism, Selfishness and Envy

This paper examines evolutionary stability of preferences by employing deterministic replicator dynamics. The preferences of players are classified into three types: altruism, selfishness, and envy. In the stage game, players compete in pairs to maximize their subjective utilities, and, as a consequence, their material payoffs are realized. We find: (i) a monomorphic population of the altruistic (the envious) has the highest (the lowest) material payoffs; and (ii) in a game between asymmetric preference types, the payoff ordering is reversed, that is, the material payoffs of the altruistic (the envious) are the lowest (the highest). We also investigate the long-run evolution process of preference types by taking the indirect evolutionary approach, under the deterministic replicator dynamics. We first show that if players' efforts are strategic complements, envy is strictly dominated, whereas altruism is strictly dominated if efforts are strategic substitutes, implying that the strictly dominated types die out in the long run. Then, we obtain our main result that there can exist a long-run stable state in which selfish players and envious players survive together if efforts are strategic substitutes, whereas there exists no long-run stable state in which altruistic players and selfish players coexist if efforts are strategic complements.

Non-cooperative game based congestion control for data rate optimization in vehicular ad hoc networks

The growth of connected vehicles in smart cities increases the number of information being communicated on the Internet of Vehicle networks. This causes wireless channel congestion problems, which degrades the network performance and reliability due to the low throughput, high average delay and the high packets loss. Therefore, this paper proposes a non-cooperative game approach to control congestion in the vehicular ad-hoc network channel where the nodes behave as selfish players requesting high data transmission rates. Moreover, the satisfaction of the Nash equilibrium condition for the optimum data transmission rate for each vehicle, is proven. A utility function is introduced based on data transmission rates, the priority of vehicles and contention delay in order to obtain the optimal rates. The performance of the proposed approach has been evaluated and validated in comparison with three others approaches over two testing scenarios for highway and urban traffic. The results show that the network performance and efficiency have been improved by an overall average of 35%, 30% and 37.17% in terms of packets loss, channel busy time and number of collision messages, respectively, as compared with the state-of-the-art-strategies for the highway testing scenario. Similar performance is achieved for the urban testing scenario.

Selfish colorful bin packing games

We consider selfish colorful bin packing games in which a set of items, each one controlled by a selfish player, are to be packed into a minimum number of unit capacity bins. Each item has one of $$m\ge 2$$ colors and no items of the same color may be adjacent in a bin. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions, i.e., the egalitarian and the proportional ones. Although, under both cost functions, these games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $$m\ge 3$$ , while they are equal to 3 when $$m=2$$ . We finally focus on the subcase of games with uniform sizes (i.e., all items have the same size). We show a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance. All of our bounds on the price of anarchy and stability hold with respect to both their absolute and asymptotic version.

Multi-round cooperative search games with multiple players

A treasure is placed in one of M boxes according to a known distribution and k searchers are searching for it in parallel during T rounds. How can one incentivize selfish players so that the probability that at least one player finds the treasure is maximized? We focus on congestion policiesC(ℓ) specifying the reward a player receives being one of the ℓ players that (simultaneously) find the treasure first. We prove that the exclusive policy, in which C(1)=1 and C(ℓ)=0 for ℓ>1, yields a price of anarchy of (1−(1−1/k)k)−1, which is the best among all symmetric reward policies. We advocate the use of symmetric equilibria, and show that besides being fair, they are highly robust to crashes of players. Indeed, in many cases, if some small fraction of players crash, symmetric equilibria remain efficient in terms of their group performance while also serving as approximate equilibria.

Interplay of Elementary Interactions Causing Social Traps in Evolutionary Games

In evolutionary games, pair interactions are defined by payoff matrices that can be decomposed into four types of orthogonal elementary games that represent fundamentally different interaction situations. The four classes of elementary interactions are formed by games with self- and cross-dependent payoffs, coordination games, and cyclic games. At the level of two-person games, social traps (dilemmas) can not occur for symmetric payoff matrices, which are combinations of coordination games and symmetrically paired self- and cross-dependent components, because individual and common interests coincide in them. In spatial evolutionary games that follow the logit evolutionary dynamics, however, the total payoff is still not maximized at certain noise levels in certain combinations of symmetric components. This phenomenon is similar to the appearance of partially ordered phases in solid state physics, which are stabilized by their higher entropy. In contrast, it is the antisymmetric part of their self- and cross-dependent components that is responsible for the emergence of traditional social dilemmas in games like the two-strategy donation game or the prisoner's dilemma. The general features of these social dilemmas are inherited by $n$-strategy games in the absence of cyclic components, which would prevent the existence of a potential and thus thermodynamic behavior. Using the mathematical framework of matrix decomposition, we survey the ways in which the interplay of elementary games can lead to a loss of total payoff for a society of selfish players. We describe the general features of different illustrative combinations of elementary games, including a game in which the presence of a cyclic component gives rise to the the tragedy of the commons via a paradoxical effect.

On weak Pareto optimality of nonatomic routing networks

This paper establishes several sufficient conditions for the weak Pareto optimality of Nash equilibria in nonatomic routing games on single- and multi-commodity networks, where a Nash equilibrium (NE) is weakly Pareto optimal (WPO) if under it no deviation of all players could make everybody better off. The results provide theoretical and technical bases for characterizing graphical structures for nonatomic routing games to admit WPO NEs. We prove that the NE of every nonatomic routing game on a single or multi-commodity network is WPO (regardless of the choices of nonnegative, continuous, nondecreasing latency functions on network links) if the network does not have two links x, y and three paths each of which goes from some origin to some destination such that the intersections of the three paths with $$\{x,y\}$$ are $$\{x\},\{y\}$$ and $$\{x,y\}$$, respectively. This sufficient condition leads to an alternative proof of the recent result that the NE of every 2-commodity nonatomic routing game on any undirected cycle is WPO. We verify a general property satisfied by all feasible 2-commodity routings (not necessarily controlled by selfish players) on undirected cycles, which roughly says that no feasible routing can “dominate” another in some sense. The property is crucial for proving the weak Pareto optimality associated to the building blocks of undirected graphs on which all NEs w.r.t. two commodities are WPO.

Social Preferences Under the Shadow of the Future

Social interactions predominantly take place under the shadow of the future. Previous literature on infinitely repeated games has highlighted the primary role of self-interested strategic considerations in explaining outcomes. Using indefinitely repeated prisoner’s dilemma games, this paper demonstrates experimentally the importance of social preferences for achieving efficient cooperative outcomes. Sorting agents by their pro-sociality, we find that cooperation is three to four times higher among prosocial players compared to selfish players. We also show that social preferences are less important when individuals interact in mixed populations. This can explain why the influence of social preferences has not been detected in previous studies.

Generalized Graph k-Coloring Games

We investigate pure Nash equilibria in generalized graphk-coloring games where we are given an edge-weighted undirected graph together with a set of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player consists of k colors. The utility of a player v in a given state or coloring is given by the sum of the weights of edges {v, u} incident to v such that the color chosen by v is different than the one chosen by u, plus the profit gained by using the chosen color. Such games form some of the basic payoff structures in game theory, model lots of real-world scenarios with selfish players and extend or are related to several fundamental class of games. We first show that generalized graph k-coloring games are potential games. In particular, they are convergent and thus Nash Equilibria always exist. We then evaluate their performance by means of the widely used notions of price of anarchy and price of stability and provide tight bounds for two natural and widely used social welfare, i.e., utilitarian and egalitarian social welfare.

Generosity, selfishness and exploitation as optimal greedy strategies for resource sharing

Resource sharing outside the kinship bonds is rare. Besides humans, it occurs in chimpanzee, wild dogs and hyenas, as well as in vampire bats. Resource sharing is an instance of animal cooperation, where an animal gives away part of the resources that it owns for the benefit of a recipient. Taking inspiration from blood-sharing in vampire bats, here we show the emergence of generosity in a Markov game, which couples the resource sharing between two players with the gathering task of that resource. At variance with the classical evolutionary models for cooperation, the optimal strategies of this game can be potentially learned by animals during their life-time. The players act greedily, that is, they try to individually maximize only their personal income. Nonetheless, the analytical solution of the model shows that three non trivial optimal behaviours emerge depending on conditions. Besides the obvious case when players are selfish in their choice of resource division, there are conditions under which both players are generous. Moreover, we also found a range of situations in which one selfish player exploits another generous individual, for the satisfaction of both players. Our results show that resource sharing is favoured by three factors: a long time horizon over which the players try to optimize their own game, the similarity among players in their ability of performing the resource-gathering task, as well as by the availability of resources in the environment. These concurrent requirements lead to identify necessary conditions for the emergence of generosity.