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The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A…
Representations are internal models of the environment that can provide guidance to a behaving agent, even in the absence of sensory information. It is not clear how representations are developed and whether or not they are necessary or…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
Past efforts to classify impartial three-player combinatorial games (the theories of Li and Straffin) have made various restrictive assumptions about the rationality of one's opponents and the formation and behavior of coalitions. One may…
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…
Game-theoretic interactions with AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to simulate an AI agent (for example because its source code is known), which…
Network games provide a natural machinery to compactly represent strategic interactions among agents whose payoffs exhibit sparsity in their dependence on the actions of others. Besides encoding interaction sparsity, however, real networks…
Two traditional paradigms are often used to describe the behavior of agents in multi-agent complex systems. In the first one, agents are considered to be fully rational and systems are seen as multi-player games. In the second one, agents…
Fairness in language models is typically studied as a property of a single, centrally optimized model. As large language models become increasingly agentic, we propose that fairness emerges through interaction and exchange. We study this…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
How much influence can a coordinated coalition exert in a multiwinner Top-$k$ election under a positional scoring rule? We study the maximum displacement problem: with coalition size $m$, how many of the current top-$k$ winners can be…
Low-level "adaptive" and higher-level "sophisticated" human reasoning processes have been proposed to play opposing roles in the emergence of unpredictable collective behaviors like crowd panics, traffic jams, and market bubbles. While…
The success of modern civilization is built upon widespread cooperation in human society, deciphering the mechanisms behind has being a major goal for centuries. A crucial fact is, however, largely missing in most prior studies that games…
We introduce a class of cooperative games induced by weighted directed graphs. Specifically, the coalitional value combines an internal interaction term given by the induced subgraph game with an external component based on minimal incoming…
We introduce Value Coalition Logic, a typed assignment-based reconstruction of classical coalition logic. The strategic semantics is unchanged: coalitional ability is still interpreted by the standard one-step game-form clause. The change…
The real world is awash with multi-agent problems that require collective action by self-interested agents, from the routing of packets across a computer network to the management of irrigation systems. Such systems have local incentives…
Natural language has the universal properties of being compositional and grounded in reality. The emergence of linguistic properties is often investigated through simulations of emergent communication in referential games. However, these…
We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…
We study the problem of partitioning a set of agents into coalitions based on the agents' additively separable preferences, which can also be viewed as a hedonic game. We apply three successively weaker solution concepts, namely…
While game theory is widely used to model strategic interactions, a natural question is where do the game representations come from? One answer is to learn the representations from data. If one wants to learn both the payoffs and the…