Browsing by Author "Sanjari, Sina"

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Open Access
Large decentralized continuous-time convex stochastic teams and their mean-field limits
(Institute of Electrical and Electronics Engineers Inc., 2024-07-12) Sanjari, Sina; Saldı, Naci; Yuksel, Serdar
We study a class of continuous-time convex stochastic exchangeable teams with a finite number of decision makers (DMs) as well as their mean-field limits with infinite numbers of DMs. We establish the existence of a globally optimal solution and show that it is Markovian and symmetric (identical) for both the finite DM regime and the infinite one. In particular, for a general class of finite-N exchangeable stochastic teams satisfying a convexity condition, we establish the existence of a globally optimal solution that is symmetric among DMs and Markovian. As the number of DMs drives to infinity (that is for the mean-field limit), we establish the existence of a possibly randomized globally optimal solution and show that it is symmetric among DMs and Markovian.
Open Access
Nash equilibria for exchangeable team-against-team games, their mean-field limit, and the role of common randomness
(Society for Industrial and Applied Mathematics, 2024-05-16) Sanjari, Sina; Saldı, Naci; Yüksel, Serdar
We study stochastic exchangeable games among a finite number of teams consisting of a large but finite number of decision makers as well as their mean-field limit with infinite number of decision makers in each team. For this class of games within static and dynamic settings, we introduce sets of randomized policies under various decentralized information structures with pri- vately independent or common randomness for decision makers within each team. (i) For a general class of exchangeable stochastic games with a finite number of decision makers, we first establish the existence of a Nash equilibrium under randomized policies (with common randomness) within each team that are exchangeable (but not necessarily symmetric, i.e., identical) among decision makers within each team. (ii) As the number of decision makers within each team goes to infinity (that is, for the mean-field limit game among teams), we show that a Nash equilibrium exists under randomized policies within each team that are independently randomized and symmetric among decision makers within each team (that is, there is no common randomness). (iii) Finally, we establish that a Nash equilibrium for a class of mean-field games among teams under independently randomized symmetric policies constitutes an approximate Nash equilibrium for the corresponding prelimit (exchangeable) game among teams with finite but large numbers of decision makers. (iv) We thus establish a rigor- ous connection between agent-based-modeling and team-against-team games, via the representative agents defining the game played in equilibrium, and we furthermore show that common randomness is not necessary for large team-against-team games, unlike the case with small-sized ones.