Approaching Utopia: Strong Truthfulness and Externality-Resistant Mechanisms

We introduce and study strongly truthful mechanisms and their applications. We use strongly truthful mechanisms as a tool for implementation in undominated strategies for several problems,including the design of externality resistant auctions and a variant of multi-dimensional scheduling

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

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

Non-Cooperative Facility Location Games: a Survey

The Facility Location problem is a well-know NP-Hard combinatorial optimization problem. It models a diverse set of situations where one aims to provide a set of goods or services via a set of facilities F to a set of clients T, also called terminals. There are opening costs for each facility in F and connection costs for each pair of facility and client, if such facility attends this client. A central authority wants to determine the solution with minimum cost, considering both opening and connection costs, in such a way that all clients are attended by one facility. In this survey we are interested in the non-cooperative game version of this problem, where instead of having a central authority, each client is a player and decides where to con- nect himself. In doing so, he aims to minimize his own costs, given by the connection costs and opening costs of the facility, which may be shared among clients using the same facility. This problem has several applications as well, specially in distributed scenarios where a central authority is too expensive or even infeasible to exist. In this paper we present a survey describing different variants of this problem and reviewing several results about it, as well as adapting results from existing literature concerning the existence of equilibria, Price of Anarchy and Price of Stability. We also point out open problems that remain to be addressed.