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In this paper, the problem of distributively seeking the equilibria of aggregative games with bilevel structures is studied. Different from the traditional aggregative games, here the aggregation is determined by the minimizer of a virtual…
Stochastic games have become a prevalent framework for studying long-term multi-agent interactions, especially in the context of multi-agent reinforcement learning. In this work, we comprehensively investigate the concept of constant-memory…
A growing body of literature in networked systems research relies on game theory and mechanism design to model and address the potential lack of cooperation between self-interested users. Most game-theoretic models applied to system…
We study an optimal targeting problem for super-modular games with binary actions and finitely many players. The considered problem consists in the selection of a subset of players of minimum size such that, when the actions of these…
Coordination in multiplayer games enables players to avoid the lose-lose outcome that often arises at Nash equilibria. However, designing a coordination mechanism typically requires the consideration of the joint actions of all players,…
In an epsilon-approximate Nash equilibrium, a player can gain at most epsilon in expectation by unilateral deviation. An epsilon well-supported approximate Nash equilibrium has the stronger requirement that every pure strategy used with…
We consider two player quadratic games in a cooperative framework known as social value orientation, motivated by the need to account for complex interactions between humans and autonomous agents in dynamical systems. Social value…
We propose a type of non-cooperative game, termed multi-cluster aggregative game, which is composed of clusters as players, where each cluster consists of collaborative agents with cost functions depending on their own decisions and the…
Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium.…
We present a new, distributed method to compute approximate Nash equilibria in bimatrix games. In contrast to previous approaches that analyze the two payoff matrices at the same time (for example, by solving a single LP that combines the…
Reinforcement learning from self-play has recently reported many successes. Self-play, where the agents compete with themselves, is often used to generate training data for iterative policy improvement. In previous work, heuristic rules are…
We study the convergence time of the best response dynamics in player-specific singleton congestion games. It is well known that this dynamics can cycle, although from every state a short sequence of best responses to a Nash equilibrium…
One of the natural objectives of the field of the social networks is to predict agents' behaviour. To better understand the spread of various products through a social network arXiv:1105.2434 introduced a threshold model, in which the nodes…
Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…
A bimatrix game $(A,B)$ is called a game of rank $k$ if the rank of the matrix $A+B$ is at most $k$. We consider the problem of enumerating the Nash equilibria in (non-degenerate) games of rank 1. In particular, we show that even for games…
Game theory is a very profound study on distributed decision-making behavior and has been extensively developed by many scholars. However, many existing works rely on certain strict assumptions such as knowing the opponent's private…
In this paper, we investigate under which conditions normal-form games are (guaranteed to be) strategically equivalent. First, we show for N-player games (N >= 3) that (A) it is NP-hard to decide whether a given strategy is a best response…
We consider a symmetric multi-players zero-sum game with two strategic variables. There are $n$ players, $n\geq 3$. Each player is denoted by $i$. Two strategic variables are $t_i$ and $s_i$, $i\in \{1, \dots, n\}$. They are related by…
We study a game between two firms in which each provide a service based on machine learning. The firms are presented with the opportunity to purchase a new corpus of data, which will allow them to potentially improve the quality of their…
The rank of a bimatrix game is defined as the rank of the sum of the payoff matrices of the two players. The rank of a game is known to impact both the most suitable computation methods for determining a solution and the expressive power of…