Stability of equilibria for population games with uncertain parameters under bounded rationality

Abstract

Under the assumption that the range of varying uncertain parameters is known, some results of existence and stability of equilibria for population games with uncertain parameters are investigated in this paper. On the basis of NS equilibria in classical noncooperative games, the concept of NS equilibria for population games with uncertain parameters is defined. Using some hypotheses about the continuity and convexity of payoff functions, the existence of NS equilibria in population games is also proved by Fan–Glicksberg fixed point theorem. Furthermore, we establish a bounded rationality model of population games with uncertain parameters, and draw the conclusions about the stability of NS equilibrium in this model by constructing the rationality function and studying its properties.

On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games

“…Khalifa and Kumar [21] investigated cooperative continuous static games in a crisp environment, defining and determining the first-kind stability set corresponding to the solution without differentiability. Under uncertainty environment, some recent researchers for cooperative games have been introduced (Mallozzi and Messalli [22], Bigdeli and Hassanpour [23], Elshafei [24], Zaichenko [25], Zidan et al [26], Donahue et al [27], Ganzfried [28], Zhou et al [29], Krishankumar et al [30,31], Tukhtasinov et al [32], Sivagami et al [33], Zhao et al [34], Megahed [35], Romanuke [36], and Khalifa et al [37]).…”

Passivity-based Analysis and Design for Population Dynamics with Conformity Biases

“…We now consider the case that (τ H − τ L ) → ∞ happens. Then, ηπ ⊤ τ + η β log l∈A exp(−βτ l ) goes to infinity due to (26). Therefore, since l∈A π l log π l is finite, S(τ, π) → ∞ holds.…”

“…However, the models dealt with in the above literature do not explicitly consider influences of biases. Although several publications [25], [26] deal with bounded rationality in population dynamics, they address the models without focusing on passivity.…”