Abstract:Cooperation in heterogeneous groups, where individuals differ in resources, productivity, and behavioural responsiveness, underpins collective action across many social and biological systems. Introspection dynamics, in which each player compares their payoff to what they would have received under the alternative action, provides a natural learning rule for such asymmetric settings.
We study introspection dynamics on multiplayer games in which the payoff difference $\Delta f_i$ evaluated by a player when considering a strategy switch is independent of all other players' current actions, a property we call state-independence. Under this condition the introspection Markov chain decomposes as a random-scan product of $N$ independent two-state chains, one per player, and the stationary distribution is a product measure. As our main application we consider the heterogeneous public goods game, where $N$ players may differ in their contributions $\alpha_i$, public goods multipliers $r_i$, and selection intensities $\beta_i$. We prove that the linear payoff structure implies state-independence, and the long-run cooperation probability admits the exact closed form
$$
p_C = \frac{1}{N}\sum_{i=1}^{N}
\left[\frac{1-\mu_{i0}-\mu_{i1}}{1+e^{\,\beta_i\alpha_i(1-r_i/N)}}+\mu_{i0}\right], $$
with no asymptotic approximation. Several structural consequences follow immediately: a player-specific cooperation threshold at $r_i = N$ (under symmetric mutation), payoff-neutrality under zero selection intensity, and the sign of each player's sensitivity to their own parameters.
| Subjects: | Computer Science and Game Theory (cs.GT) |
| MSC classes: | 91A22, 91A26 |
| ACM classes: | G.3 |
| Cite as: | arXiv:2605.23513 [cs.GT] |
| (or arXiv:2605.23513v1 [cs.GT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23513 arXiv-issued DOI via DataCite (pending registration) |
From: Vincent Knight Prof. [view email]
[v1]
Fri, 22 May 2026 11:23:27 UTC (171 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。