Learning Equilibria in Matching Games with Bandit Feedback
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915324751773696 |
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| author | Athanasopoulos, Andreas Dimitrakakis, Christos |
| author_facet | Athanasopoulos, Andreas Dimitrakakis, Christos |
| contents | We investigate the problem of learning an equilibrium in a generalized two-sided matching market, where agents can adaptively choose their actions based on their assigned matches. Specifically, we consider a setting in which matched agents engage in a zero-sum game with initially unknown payoff matrices, and we explore whether a centralized procedure can learn an equilibrium from bandit feedback. We adopt the solution concept of matching equilibrium, where a pair consisting of a matching $\mathfrak{m}$ and a set of agent strategies $X$ forms an equilibrium if no agent has the incentive to deviate from $(\mathfrak{m}, X)$. To measure the deviation of a given pair $(\mathfrak{m}, X)$ from the equilibrium pair $(\mathfrak{m}^\star, X^\star)$, we introduce matching instability that can serve as a regret measure for the corresponding learning problem. We then propose a UCB algorithm in which agents form preferences and select actions based on optimistic estimates of the game payoffs, and prove that it achieves sublinear, instance-independent regret over a time horizon $T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Equilibria in Matching Games with Bandit Feedback Athanasopoulos, Andreas Dimitrakakis, Christos Machine Learning We investigate the problem of learning an equilibrium in a generalized two-sided matching market, where agents can adaptively choose their actions based on their assigned matches. Specifically, we consider a setting in which matched agents engage in a zero-sum game with initially unknown payoff matrices, and we explore whether a centralized procedure can learn an equilibrium from bandit feedback. We adopt the solution concept of matching equilibrium, where a pair consisting of a matching $\mathfrak{m}$ and a set of agent strategies $X$ forms an equilibrium if no agent has the incentive to deviate from $(\mathfrak{m}, X)$. To measure the deviation of a given pair $(\mathfrak{m}, X)$ from the equilibrium pair $(\mathfrak{m}^\star, X^\star)$, we introduce matching instability that can serve as a regret measure for the corresponding learning problem. We then propose a UCB algorithm in which agents form preferences and select actions based on optimistic estimates of the game payoffs, and prove that it achieves sublinear, instance-independent regret over a time horizon $T$. |
| title | Learning Equilibria in Matching Games with Bandit Feedback |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.03802 |