Behavioral deviations from subjective expected utility theory, most famously captured by the Allais paradox (Allais, 1953) and the Ellsberg paradox (Ellsberg, 1961), have inspired extensive theoretical and experimental research into risk and ambiguity preferences. While the existing studies (e.g., Gilboa and Schmeidler, 1989; Machina, 2009) analyze these paradoxes independently, little work explores how such heterogeneously biased agents interact in networked strategic environments. Our paper fills this gap by modeling a convergent Markov–network game between Allais-type and Ellsberg-type players, each endowed with fully enriched loss matrices that reflect their distinct probabilistic and ambiguity attitudes.

We define convergent priors as those inducing a spectral radius of < 1 in iterated enriched matrices, ensuring iterative convergence under a matrix-based update rule. Players minimize their losses under these priors in each iteration, converging to an equilibrium where no further updates are feasible. We analyze this convergence under three learning regimes—homophily, heterophily, and type-neutral randomness—each defined via distinct neighborhood learning dynamics. To validate the equilibrium, we construct a risk-neutral measure by transforming losses into payoffs and derive a riskless rate of return representing players' subjective indifference to risk. This applies risk-neutral pricing logic to behavioral matrices, which is novel.

This framework unifies paradox-type decision makers within a networked Markovian environment (stochastic adjacency matrix), extending models of dynamic learning (e.g., Bala and Goyal, 1998; Golub, 2012; Gale and Kariv, 2003) and providing a novel equilibrium characterization for heterogeneous, ambiguity-averse agents in structured interactions.

Keywords: convergent priors; Markov–network game, Allais-type; Ellsberg-type