This paper investigates the strategic and welfare properties of endogenous population partitioning (secession) within large-population anonymous games featuring strategic heterogeneity. We consider a continuum-player framework with a binary action space where players are categorized either as fol- lowers, who experience positive network externalities from conformity, or as contrarians, who seek distinctiveness via anti-conformism. We fully characterize the set of Nash equilibria and establish con- ditions under which costless secession yields structural Pareto improvements. We demonstrate that in any strategically mixed society, every mixed-strategy Nash equilibrium admits a Pareto-improving se- cession. With finitely many types, secession systematically mitigates coordination frictions, enhancing both individual payoffs and aggregate utility. Furthermore, we characterize social planner configura- tions optimizing weighted aggregate utility, establishing a formal mathematical isomorphism between optimal jurisdictional design and the theory of Bayesian persuasion solved via concavification. Finally, we derive the structural conditions governing migration stability when subgroups can unilaterally re- locate across distinct societies.
Can altruism serve as the behavioral foundation for efficient institutional design? We study full implementation in Berge equilibrium, the solution concept that formalizes strategic altruism: each agent's opponents collectively maximize her payoff. While Berge equilibrium resolves the Prisoner's Dilemma and can eliminate cooperation failures in social dilemmas, we show that this optimism does not survive the move from individual behavior to institutional design. First, we show that the weak Pareto optimal rule is not implementable in Berge equilibrium. Second, on the unrestricted domain of strict preferences, any social choice rule that is both weakly Pareto efficient and implementable in Berge equilibrium must be dictatorial. Finally, we show that Berge implementability is strictly more demanding than Nash implementability: every social goal achievable under strategic altruism is also achievable under self-interest, but not vice versa. The very feature that makes Berge equilibrium appealing at the behavioral level, that is, opponents protecting each agent's payoff, is precisely what forecloses efficient, non-dictatorial institutions at the design level.
Foivos Savva, M. Lombardi, Ritesh Jain· 0 citations
Majoritarian democracy is widely regarded as the canonical procedure for converting heterogeneous individual preferences into collective decisions, yet its welfare properties are far more fragile than legal and political theorists suggest. This paper contributes to the literature on the limits of majoritarianism by applying a spatial voting model to demonstrate that the conditions under which majoritarian democracies produce efficient outcomes are narrowly constrained by the structural features of majority rule itself. We formalize a multidimensional policy environment in which voters bargain over both the policy vector and lump‑sum transfers. We show that—even with transferable utility among members of the majority coalitions—the equilibrium chosen by the pivotal majority is generally off the Pareto frontier. Taken together, these results establish an impossibility theorem for majority rule in multidimensional policy spaces: whether coalitions are stable or cyclical, simple majority voting fails to maximize aggregate welfare. Political externalities imposed on minorities systematically exceed the surplus gains accruing to decisive majorities, and vote trading cannot redress the loss. Institutional remedies—supermajority thresholds, agenda control, or issue-bundling constraints—are therefore necessary conditions for approaching efficiency under democratic decision-making.
Barbara Luppi, F. Parisi· Public Choice· 0 citations
The public goods game (PGG) serves as a powerful framework for investigating human cooperative behavior. While prevailing theories emphasize imitation as the primary driver of strategy updating, evidence from an empirical study on voluntary spatial PGG revealed that human decision adjustments correlate more closely with historical payoffs than with imitative behavior. The objective of this study is to validate this conclusion and to quantify the optimal strategy-updating parameters through computational modeling. We develop an agent-based model on a square lattice with periodic boundary conditions, integrating prospect theory with a mixed-strategy evolutionary framework. The model systematically examines the effects of the proportion of self-adjustment (POS), mutation rate (MIS), and sensitivity coefficient (SEN) on the stationary distribution of cooperators, defectors, and loners. Our main findings demonstrate that individuals update strategies primarily through self-adjustment based on historical payoffs, with imitation playing merely an auxiliary role. The optimal self-adjustment proportion is approximately 0.9, and low sensitivity coefficients and mutation rates favor the emergence of cooperation. These results provide quantitative support for the memory-based self-regulation mechanism and offer managerial insights into promoting cooperation in social dilemma situations.
Hao-Chen Wu, Meng-Cheng Sun, Lu-He Yang et al.· Games· 0 citations
We study a mechanism of cooperation in the Prisoner's Dilemma (PD). Incorporating social preferences as efficiency concerns into the PD game, we study how altruism translates into cooperation. Under complete information, cooperation requires the opponent's altruism to clear a threshold. We then introduce a subjective extension of Bayesian Nash equilibrium that relaxes the Common Prior Assumption, letting players hold heterogeneous, potentially misspecified beliefs about each other's altruistic type. Cooperation then depends on beliefs about altruism rather than altruism itself, and can be sustained even when opponents are, on average, only weakly altruistic. When fear of exploitation dominates the temptation to defect, beliefs about the opponent's cooperation become strategic complements, so a cooperative and an uncooperative equilibrium can coexist under identical payoffs and an identical, correctly specified prior. Using multiplier preferences, we then study how robust this belief-driven cooperation is to model misspecification. Cooperation is fragile: it survives only above a threshold level of confidence in one's own belief, and can unravel even when the belief itself correctly supports cooperation. As a formal extension, the same robust-control apparatus, applied to a player's action choice, nests Nash equilibrium, Bayesian Nash equilibrium, and logit Quantal Response Equilibrium as limiting cases. Cooperation depends less on how altruistic agents are than on what they believe about each other, and how confident they are that this belief is right.
Which social norms are self-correcting under rational learning? We show that conduct sustained by false beliefs cannot persist if a single departure from prevailing behavior generates evidence against those beliefs. We study the overlapping-generations learning model of Fudenberg and Levine (1993), in which finitely lived Bayesian agents are repeatedly and randomly matched with agents in other player roles, observe only their own matches, and learn from experience. In simple extensive-form games with nodewise-independent, nondegenerate priors, as agents live increasingly long lives and become sufficiently patient, every limiting game outcome is path-equivalent to a subgame-confirmed equilibrium. This establishes the converse of Fudenberg and Levine (2006). The mechanism is endogenous experimentation: uncertainty about the consequences of a potentially profitable departure gives patient agents an incentive to test it, generating the observations that correct beliefs and discipline continuation play.
Strategic decision-making in networked systems unfolds sequentially, with each agent’s choice shaped by the observable actions of those who decide earlier. We extend bounded rationality from simultaneous to sequential decision structures on scale-free networks, showing how modified backward induction yields approximate subgame perfect equilibria that converge to their exact counterparts as the rationality parameter increases, forming bounded-rationality refinements of Nash equilibria. Agents ordered by network centrality condition on their predecessors’ actions through a centrality-weighted observation term, with social learning and strategic exploration jointly defining a behavioral regime that ranges from winner-takes-all configurations concentrated among hub agents to broader participation with flattened centrality gradients. In the four equilibrium scenarios examined, the sequential protection distribution stochastically dominates the simultaneous baseline, and centrality-based ordering outperforms random and inverse alternatives. Cross-domain calibration against banking, epidemiological, and sports network data shows that introducing the observation term strengthens the centrality–protection correlation in all three domains, consistent with a common mechanism operating across distinct behavioral systems.
Chulwook Park· Scientific Reports· 0 citations
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