Budget-restricted utility games with ordered strategic decisions

We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to be shared between the tasks. We study strategic budget games, where the budget is shared proportionally. We also consider a variant in which the order of the strategic decisions influences the distribution of the budgets. The complexity of the optimal solution as well as existence, complexity and quality of equilibria are analyzed. Finally, we show that the time an ordered budget game needs to convergence towards an equilibrium may be exponential

Dominance-Solvable Lattice Games

This paper derives sufficient and necessary conditions for dominance-solvability of so-called lattice games whose strategy sets have a lattice structure while they simultaneously belong to some metric space. The argument combines and extends Moulin's (1984) approach for nice games and Milgrom and Roberts' (1990) approach for supermodular games. The analysis covers - but is not restricted to - the case of actions being strategic complements as well as the case of actions being strategic substitutes. Applications are given for n-firm Cournot oligopolies, auctions with bidders who are optimistic - respectively pessimistic - with respect to an imperfectly known allocation rule, and Two-player Bayesian models of bank runs.

Under-connected and Over-connected Networks

Since the seminal contribution of Jackson & Wolinsky 1996 [A Strategic Model of Social and Economic Networks, JET 71, 44-74] it has been widely acknowledged that the formation of social networks exhibits a general conflict between individual strategic behavior and collective outcome. What has not been studied systematically are the sources of inefficiency. We approach this omission by analyzing the role of positive and negative externalities of link formation. This yields general results that relate situations of positive externalities with stable networks that cannot be “too dense” in a well-defined sense, while situations with negative externalities tend to induce “too dense” networks.Networks, Network Formation, Connections, Game Theory, Externalities, Spillovers, Stability, Efficiency

Dominance-solvable lattice games

This paper derives sufficient and necessary conditions for dominance-solvability of so-called lattice games whose strategy sets have a lattice structure while they simultaneously belong to some metric space. The argument combines and extends Moulin's (1984) approach for nice games and Milgrom and Roberts' (1990) approach for supermodular games. The analysis covers - but is not restricted to - the case of actions being strategic complements as well as the case of actions being strategic substitutes. Applications are given for n-firm Cournot oligopolies, auctions with bidders who are optimistic - respectively pessimistic - with respect to an imperfectly known allocation rule, and Two-player Bayesian models of bank runs

On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

Elicited beliefs and social information in modified dictator games: What do dictators believe other dictators do?

We use subjects’ actions in modified dictator games to perform a within-subject classification of individuals into four different types of interdependent preferences: Selfish, Social Welfare maximizers, Inequity Averse and Competitive. We elicit beliefs about other subjects’ actions in the same modified dictator games to test how much of the existent heterogeneity in others’ actions is known by subjects. We find that subjects with different interdependent preferences in fact have different beliefs about others’ actions. In particular, Selfish individuals cannot conceive others being non-Selfish while Social Welfare maximizers are closest to the actual distribution of others’ actions. We finally provide subjects with information on other subjects’ actions and re-classify individuals according to their (new) actions in the same modified dictator games. We find that social information does not affect Selfish individuals, but that individuals with interdependent preferences are more likely to change their behavior and tend to behave more selfishly.Interdependent preferences, social welfare maximizing, inequity aversion, belief elicitation, social information, experiments, mixture-of-types models, LeeX