Related papers: Matching Games with Additive Externalities
A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…
This paper develops a mean field game framework for dynamic two-sided matching markets, extending existing matching theory by integrating micro-macro dynamics in two-sided environments. Unlike traditional matching models focusing on static…
In this paper I discuss truthful equilibria in common agency models. Specifically, I provide general conditions under which truthful equilibria are plausible, easy to calculate and efficient. These conditions generalize similar results in…
We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this…
Stable matching is a fundamental area with many practical applications, such as centralised clearinghouses for school choice or job markets. Recent work has introduced the paradigm of near-feasibility in capacitated matching settings, where…
We introduce a model of dynamic matching with transferable utility, extending the static model of Shapley and Shubik (1971). Forward-looking agents have individual states that evolve with current matches. Each period, a matching market with…
Strategy-proof mechanisms are widely used in market design. In an abstract allocation framework where outside options are available to agents, we obtain two results for strategy-proof mechanisms. They provide a unified foundation for…
We examine the effects of introducing a political outsider to the nomination process leading to an election. To this end, we develop a sequential game where politicians -- insiders and outsiders -- make a platform offer to a party, and…
We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- in which for each…
How can one detect friendly and adversarial behavior from raw data? Detecting whether an environment is a friend, a foe, or anything in between, remains a poorly understood yet desirable ability for safe and robust agents. This paper…
Most of the existing algorithms for fair division do not consider externalities. Under externalities, the utility an agent obtains depends not only on its allocation but also on the allocation of other agents. An agent has a positive…
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…
Although the integration of two-sided matching markets using stable mechanisms generates expected gains from integration, I show that there are worst-case scenarios in which these are negative. The losses from integration can be large…
The Deferred Acceptance (DA) algorithm is an elegant procedure for finding a stable matching in two-sided matching markets. It ensures that no pair of agents prefers each other to their matched partners. In this work, we initiate the study…
We study the Popular Matching problem in multiple models, where the preferences of the agents in the instance may change or may be unknown/uncertain. In particular, we study an Uncertainty model, where each agent has a possible set of…
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least…
We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are…
This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and…
We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…
Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a…