Smooth Information Gathering in Two-Player Noncooperative Games
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912084775665664 |
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| author | Palafox, Fernando Milzman, Jesse Lee, Dong Ho Park, Ryan Fridovich-Keil, David |
| author_facet | Palafox, Fernando Milzman, Jesse Lee, Dong Ho Park, Ryan Fridovich-Keil, David |
| contents | We present a mathematical framework for modeling two-player noncooperative games in which one player is uncertain of the other player's costs but can preemptively allocate information-gathering resources to reduce this uncertainty. We refer to the players as the uncertain player (UP) and the certain player (CP), respectively. We obtain UP's decisions by solving a two-stage problem where, in Stage 1, UP allocates information-gathering resources that smoothly transform the information structure in the second stage. Then, in Stage 2, a signal (that is, a function of the Stage 1 allocation) informs UP about CP's costs, and both players execute strategies which depend upon the signal's value. This framework allows for a smooth resource allocation, in contrast to existing literature on the topic. We also identify conditions under which the gradient of UP's overall cost with respect to the information-gathering resources is well-defined. Then we provide a gradient-based algorithm to solve the two-stage game. Finally, we apply our framework to a tower-defense game which can be interpreted as a variant of a Colonel Blotto game with smooth payoff functions and uncertainty over battlefield valuations. We include an analysis of how optimal decisions shift with changes in information-gathering allocations and perturbations in the cost functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00733 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smooth Information Gathering in Two-Player Noncooperative Games Palafox, Fernando Milzman, Jesse Lee, Dong Ho Park, Ryan Fridovich-Keil, David Computer Science and Game Theory Multiagent Systems Systems and Control We present a mathematical framework for modeling two-player noncooperative games in which one player is uncertain of the other player's costs but can preemptively allocate information-gathering resources to reduce this uncertainty. We refer to the players as the uncertain player (UP) and the certain player (CP), respectively. We obtain UP's decisions by solving a two-stage problem where, in Stage 1, UP allocates information-gathering resources that smoothly transform the information structure in the second stage. Then, in Stage 2, a signal (that is, a function of the Stage 1 allocation) informs UP about CP's costs, and both players execute strategies which depend upon the signal's value. This framework allows for a smooth resource allocation, in contrast to existing literature on the topic. We also identify conditions under which the gradient of UP's overall cost with respect to the information-gathering resources is well-defined. Then we provide a gradient-based algorithm to solve the two-stage game. Finally, we apply our framework to a tower-defense game which can be interpreted as a variant of a Colonel Blotto game with smooth payoff functions and uncertainty over battlefield valuations. We include an analysis of how optimal decisions shift with changes in information-gathering allocations and perturbations in the cost functions. |
| title | Smooth Information Gathering in Two-Player Noncooperative Games |
| topic | Computer Science and Game Theory Multiagent Systems Systems and Control |
| url | https://arxiv.org/abs/2404.00733 |