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on Sports and Economics |
| By: | Marcin Dziubi\'nski |
| Abstract: | We study equilibrium strategies and the value of the asymmetric variant of the discrete Colonel Blotto game with $K \geq 2$ battlefields, $B \geq 1$ resources of the weaker player and $A > B$ resources of the stronger player. We derive equilibrium strategies and the formulas for the value of the game for the cases where the number of resources of the weaker player, $B$, is at least $2(\lceil A/K \rceil - 1)$ as well as for the cases where this number is at most $\lfloor A/K \rfloor$. In particular, we solve all the cases of the game which can be solved using the discrete General Lotto game of~\cite{Hart08}. We propose a constrained variant of the discrete General Lotto game and use it to derive equilibrium strategies in the discrete Colonel Blotto game, that go beyond the General Lotto solvable cases game. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.10827 |
| By: | Argyrios Deligkas; Gregory Gutin; Mark Jones; Philip R. Neary; Anders Yeo |
| Abstract: | In a public goods game, every player chooses whether or not to buy a good that all neighboring players will have access to. We consider a setting in which the good is indivisible, neighboring players are out-neighbors in a directed graph, and there is a capacity constraint on their number, k, that can benefit from the good. This means that each player makes a two-pronged decision: decide whether or not to buy and, conditional on buying, choose which k out-neighbors to share access. We examine both pure and mixed Nash equilibria in the model from the perspective of existence, computation, and efficiency. We perform a comprehensive study for these three dimensions with respect to both sharing capacity (k) and the network structure (the underlying directed graph), and establish sharp complexity dichotomies for each. |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2511.11475 |