Unilateral Altruism in Network Routing Games with Atomic Players

We study a routing game in which one of the players unilaterally acts altruistically by taking into consideration the latency cost of other players as well as his own. By not playing selfishly, a player can not only improve the other players' equilibrium utility but also improve his own equilibrium utility. To quantify the effect, we define a metric called the Value of Unilateral Altruism (VoU) to be the ratio of the equilibrium utility of the altruistic user to the equilibrium utility he would have received in Nash equilibrium if he were selfish. We show by example that the VoU, in a game with nonlinear latency functions and atomic players, can be arbitrarily large. Since the Nash equilibrium social welfare of this example is arbitrarily far from social optimum, this example also has a Price of Anarchy (PoA) that is unbounded. The example is driven by there being a small number of players since the same example with non-atomic players yields a Nash equilibrium that is fully efficient

Selfishness, altruism and message spreading in mobile social networks

Many kinds of communication networks, in particular social and opportunistic networks, rely at least partly on on humans to help move data across the network. Human altruistic behavior is an important factor determining the feasibility of such a system. In this paper, we study the impact of different distributions of altruism on the throughput and delay of mobile social communication system. We evaluate the system performance using four experimental human mobility traces with uniform and community-biased traffic patterns. We found that mobile social networks are very robust to the distributions of altruism due to the nature of multiple paths. We further confirm the results by simulations on two popular social network models. To the best of our knowledge, this is the first complete study of the impact of altruism on mobile social networks, including the impact of topologies and traffic patterns.published_or_final_versio

Selfishness Level of Strategic Games

We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games. We study the selfishness level of several well-known strategic games. This allows us to quantify the implicit tension within a game between players' individual interests and the impact of their decisions on the society as a whole. Our analyses reveal that the selfishness level often provides a deeper understanding of the characteristics of the underlying game that influence the players' willingness to cooperate. In particular, the selfishness level of finite ordinal potential games is finite, while that of weakly acyclic games can be infinite. We derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which depend on specific parameters of the underlying game but are independent of the number of players. Further, we show that the selfishness level of the $n$-players Prisoner's Dilemma is $c/(b(n-1)-c)$, where $b$ and $c$ are the benefit and cost for cooperation, respectively, that of the $n$-players public goods game is $(1-\frac{c}{n})/(c-1)$, where $c$ is the public good multiplier, and that of the Traveler's Dilemma game is $\frac{1}{2}(b-1)$, where $b$ is the bonus. Finally, the selfishness level of Cournot competition (an example of an infinite ordinal potential game, Tragedy of the Commons, and Bertrand competition is infinite.Comment: 34 page

Comparative Statics of Altruism and Spite

The equilibrium outcome of a strategic interaction between two or more people may depend on the weight they place on each other’s payoff. A positive, negative or zero weight represents altruism, spite or complete selfishness, respectively. Paradoxically, the real, material payoff in equilibrium for a group of altruists may be lower than for selfish or spiteful groups. However, this can only be so if the equilibria involved are unstable. If they are stable, the total (equivalently, average) payoff can only increase or remain unchanged with an increasing degree of altruism.Altruism, spite, comparative statics, strategic games, stability of equilibrium

Bounding the Inefficiency of Altruism Through Social Contribution Games

We introduce a new class of games, called social contribution games (SCGs), where each player's individual cost is equal to the cost he induces on society because of his presence. Our results reveal that SCGs constitute useful abstractions of altruistic games when it comes to the analysis of the robust price of anarchy. We first show that SCGs are altruism-independently smooth, i.e., the robust price of anarchy of these games remains the same under arbitrary altruistic extensions. We then devise a general reduction technique that enables us to reduce the problem of establishing smoothness for an altruistic extension of a base game to a corresponding SCG. Our reduction applies whenever the base game relates to a canonical SCG by satisfying a simple social contribution boundedness property. As it turns out, several well-known games satisfy this property and are thus amenable to our reduction technique. Examples include min-sum scheduling games, congestion games, second price auctions and valid utility games. Using our technique, we derive mostly tight bounds on the robust price of anarchy of their altruistic extensions. For the majority of the mentioned game classes, the results extend to the more differentiated friendship setting. As we show, our reduction technique covers this model if the base game satisfies three additional natural properties

Altruism in Atomic Congestion Games

This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting increase in social cost. Our model can be embedded in the framework of congestion games with player-specific latency functions. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. Previous work shows that for symmetric singleton games with convex delays Nash equilibria are guaranteed to exist. For concave delay functions we observe that there are games without Nash equilibria and provide a polynomial time algorithm to decide existence for symmetric singleton games with arbitrary delay functions. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, then there is always a Nash equilibrium in any congestion game with altruists and any better-response dynamics converges. In addition to these results for uncoordinated dynamics, we consider a scenario in which a central altruistic institution can motivate agents to act altruistically. We provide constructive and hardness results for finding the minimum number of altruists to stabilize an optimal congestion profile and more general mechanisms to incentivize agents to adopt favorable behavior.Comment: 13 pages, 1 figure, includes some minor adjustment