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Register a new userNo-regret Learning in Cournot Games
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Added by
Yuanyuan Shi
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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This paper examines the convergence of no-regret learning in Cournot games with continuous actions. Cournot games are the essential model for many socio-economic systems, where players compete by strategically setting their output quantity. We assume that players do not have full information of the game and thus cannot pre-compute a Nash equilibrium. Two types of feedback are considered: one is bandit feedback and the other is gradient feedback. To study the convergence of the induced sequence of play, we introduce the notion of convergence in measure, and show that the players actual sequence of action converges to the unique Nash equilibrium. In addition, our results naturally extend the no-regret learning algorithms time-average regret bounds to obtain the final-iteration convergence rates. Together, our work presents significantly sharper convergence results for learning in games without strong assumptions on game property (e.g., monotonicity) and shows how exploiting the game information feedback can influence the convergence rates.
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Counterfactual Regret Minimization (CFR) is an efficient no-regret learning algorithm for decision problems modeled as extensive games. CFRs regret bounds depend on the requirement of perfect recall: players always remember information that was revealed to them and the order in which it was revealed. In games without perfect recall, however, CFRs guarantees do not apply. In this paper, we present the first regret bound for CFR when applied to a general class of games with imperfect recall. In addition, we show that CFR applied to any abstraction belonging to our general class results in a regret bound not just for the abstract game, but for the full game as well. We verify our theory and show how imperfect recall can be used to trade a small increase in regret for a significant reduction in memory in three domains: die-roll poker, phantom tic-tac-toe, and Bluff.
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This paper considers repeated games in which one player has more information about the game than the other players. In particular, we investigate repeated two-player zero-sum games where only the column player knows the payoff matrix A of the game. Suppose that while repeatedly playing this game, the row player chooses her strategy at each round by using a no-regret algorithm to minimize her (pseudo) regret. We develop a no-instant-regret algorithm for the column player to exhibit last round convergence to a minimax equilibrium. We show that our algorithm is efficient against a large set of popular no-regret algorithms of the row player, including the multiplicative weight update algorithm, the online mirror descent method/follow-the-regularized-leader, the linear multiplicative weight update algorithm, and the optimistic multiplicative weight update.
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In this paper, we consider a distributed learning problem in a subnetwork zero-sum game, where agents are competing in different subnetworks. These agents are connected through time-varying graphs where each agent has its own cost function and can receive information from its neighbors. We propose a distributed mirror descent algorithm for computing a Nash equilibrium and establish a sublinear regret bound on the sequence of iterates when the graphs are uniformly strongly connected and the cost functions are convex-concave. Moreover, we prove its convergence with suitably selected diminishing stepsizes for a strictly convex-concave cost function. We also consider a constant step-size variant of the algorithm and establish an asymptotic error bound between the cost function values of running average actions and a Nash equilibrium. In addition, we apply the algorithm to compute a mixed-strategy Nash equilibrium in subnetwork zero-sum finite-strategy games, which have merely convex-concave (to be specific, multilinear) cost functions, and obtain a final-iteration convergence result and an ergodic convergence result, respectively, under different assumptions.
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