An Equilibrium Analysis of the Arad-Rubinstein Game
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929292298944512 |
|---|---|
| author | Ewerhart, Christian Kaźmierowski, Stanisław |
| author_facet | Ewerhart, Christian Kaźmierowski, Stanisław |
| contents | Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the tie-breaking rule is allowed to be flexible. We begin by pointing out that equilibrium constructions known from the literature extend to our class of games. However, we also note that irrespective of the tie-breaking rule, the equilibrium set is excessively large. Specifically, any pure strategy that allocates at most twice the fair share to each battlefield is used with positive probability in some equilibrium. Furthermore, refinements based on the elimination of weakly dominated strategies prove ineffective. To derive specific predictions amid this multiplicity, we compute strategies resulting from long-run adaptive learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Equilibrium Analysis of the Arad-Rubinstein Game Ewerhart, Christian Kaźmierowski, Stanisław Computer Science and Game Theory 91A05 J.4 Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the tie-breaking rule is allowed to be flexible. We begin by pointing out that equilibrium constructions known from the literature extend to our class of games. However, we also note that irrespective of the tie-breaking rule, the equilibrium set is excessively large. Specifically, any pure strategy that allocates at most twice the fair share to each battlefield is used with positive probability in some equilibrium. Furthermore, refinements based on the elimination of weakly dominated strategies prove ineffective. To derive specific predictions amid this multiplicity, we compute strategies resulting from long-run adaptive learning. |
| title | An Equilibrium Analysis of the Arad-Rubinstein Game |
| topic | Computer Science and Game Theory 91A05 J.4 |
| url | https://arxiv.org/abs/2403.17139 |