27 research outputs found

    The curse of ties in congestion games with limited lookahead

    Get PDF
    We introduce a novel framework to model limited lookahead in congestion games. Intuitively, the players enter the game sequentially and choose an optimal action under the assumption that the k - 1 subsequent players play subgame-perfectly. Our model naturally interpolates between outcomes of greedy best-response (k = 1) and subgame-perfect outcomes (k = n, the number of players). We study the impact of limited lookahead (parameterized by k) on the stability and inefficiency of the resulting outcomes. As our results reveal, increased lookahead does not necessarily lead to better outcomes; in fact, its effect crucially depends on the existence of ties and the type of game under consideration

    Convergence of Incentive-Driven Dynamics in Fisher Markets

    Get PDF
    In both general equilibrium theory and game theory, the dominant mathematical models rest on a fully rational solution concept in which every player's action is a best-response to the actions of the other players. In both theories there is less agreement on suitable out- of-equilibrium modeling, but one attractive approach is the level k model in which a level 0 player adopts a very simple response to current conditions, a level 1 player best-responds to a model in which others take level 0 actions, and so forth. (This is analogous to k-ply exploration of game trees in AI, and to receding-horizon control in control theory.) If players have deterministic mental models with this kind of finite-level response, there is obviously no way their mental models can all be consistent. Nevertheless, there is experimental evidence that people act this way in many situations, motivating the question of what the dynamics of such interactions lead to. We address the problem of out-of-equilibrium price dynamics in the setting of Fisher markets. We develop a general framework in which sellers have (a) a set of atomic price update rules which are simple responses to a price vector; (b) a belief-formation procedure that simulates actions of other sellers (themselves using the atomic price updates) to some finite horizon in the future. In this framework, sellers use an atomic price update rule to respond to a price vector they generate with the belief formation procedure. The framework is general and allows sellers to have inconsistent and time- varying beliefs about each other. Under certain assumptions on the atomic update rules, we show that despite the inconsistent and time-varying nature of beliefs, the market converges to a unique equilibrium. (If the price updates are driven by weak-gross substitutes demands, this is the same equilibrium point predicted by those demands.) This result holds for both synchronous and asynchronous discrete-time updates. Moreover, the result is computationally feasible in the sense that the convergence rate is linear, i.e., the distance to equilibrium decays exponentially fast. To the best of our knowledge, this is the first result that demonstrates, in Fisher markets, convergence at any rate for dynamics driven by a plausible model of seller incentives. We then specialize our results to Fisher markets with elastic demands (a further special case corresponds to demand generated by buyers with constant elasticity of substitution (CES) utilities, in the weak gross substitutes (WGS) regime) and show that the atomic update rule in which a seller uses the best-response (=profit- maximizing) update given the prices of all other sellers, satisfies the assumptions required on atomic price update rules in our framework. We can even characterize the convergence rate (as a function of elasticity parameters of the demand function). Our results apply also to settings where, to the best of our knowledge, there exists no previous demonstration of efficient convergence of any discrete dynamic of price updates. Even for the simple case of (level 0) best- response dynamics, our result is the first to demonstrate a linear rate of convergence

    Convergence of Incentive-Driven Dynamics in Fisher Markets

    Get PDF
    In both general equilibrium theory and game theory, the dominant mathematical models rest on a fully rational solution concept in which every player's action is a best-response to the actions of the other players. In both theories there is less agreement on suitable out- of-equilibrium modeling, but one attractive approach is the level k model in which a level 0 player adopts a very simple response to current conditions, a level 1 player best-responds to a model in which others take level 0 actions, and so forth. (This is analogous to k-ply exploration of game trees in AI, and to receding-horizon control in control theory.) If players have deterministic mental models with this kind of finite-level response, there is obviously no way their mental models can all be consistent. Nevertheless, there is experimental evidence that people act this way in many situations, motivating the question of what the dynamics of such interactions lead to. We address the problem of out-of-equilibrium price dynamics in the setting of Fisher markets. We develop a general framework in which sellers have (a) a set of atomic price update rules which are simple responses to a price vector; (b) a belief-formation procedure that simulates actions of other sellers (themselves using the atomic price updates) to some finite horizon in the future. In this framework, sellers use an atomic price update rule to respond to a price vector they generate with the belief formation procedure. The framework is general and allows sellers to have inconsistent and time- varying beliefs about each other. Under certain assumptions on the atomic update rules, we show that despite the inconsistent and time-varying nature of beliefs, the market converges to a unique equilibrium. (If the price updates are driven by weak-gross substitutes demands, this is the same equilibrium point predicted by those demands.) This result holds for both synchronous and asynchronous discrete-time updates. Moreover, the result is computationally feasible in the sense that the convergence rate is linear, i.e., the distance to equilibrium decays exponentially fast. To the best of our knowledge, this is the first result that demonstrates, in Fisher markets, convergence at any rate for dynamics driven by a plausible model of seller incentives. We then specialize our results to Fisher markets with elastic demands (a further special case corresponds to demand generated by buyers with constant elasticity of substitution (CES) utilities, in the weak gross substitutes (WGS) regime) and show that the atomic update rule in which a seller uses the best-response (=profit- maximizing) update given the prices of all other sellers, satisfies the assumptions required on atomic price update rules in our framework. We can even characterize the convergence rate (as a function of elasticity parameters of the demand function). Our results apply also to settings where, to the best of our knowledge, there exists no previous demonstration of efficient convergence of any discrete dynamic of price updates. Even for the simple case of (level 0) best- response dynamics, our result is the first to demonstrate a linear rate of convergence

    The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing

    Get PDF
    This paper provides new bounds on the quality of equilibria in finite congestion games with affine cost functions, specifically for atomic network routing games. It is well known that the price of anarchy equals exactly 5/2 in general. For symmetric network routing games, it is at most (5n−2)/(2n+ 1), where n is the number of players. The paper answers to two open questions for congestion games. First, we show that the price of anarchy bound (5n−2)/(2n+ 1) is tight for symmetric network routing games, thereby answering a decade-old open question. Secondly, we ask if sequential play and subgame perfection allows to evade worst-case Nash equilibria, and thereby reduces the price of anarchy. This is motivated by positive results for congestion games with a small number of players, as well as recent results for other resource allocation problems. Our main result is the perhaps surprising proof that subgame perfect equilibria of sequential symmetric network routing games with linear cost functions can have an unbounded price of anarchy. We complete the picture by analyzing the case with two players: We show that the sequential price of anarchy equals 7/5, and that computing the outcome of a subgame perfect equilibrium is NP-hard

    Dynamic pricing with demand learning under competition

    Get PDF
    Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 199-204).In this thesis, we focus on oligopolistic markets for a single perishable product, where firms compete by setting prices (Bertrand competition) or by allocating quantities (Cournot competition) dynamically over a finite selling horizon. The price-demand relationship is modeled as a parametric function, whose parameters are unknown, but learned through a data driven approach. The market can be either in disequilibrium or in equilibrium. In disequilibrium, we consider simultaneously two forms of learning for the firm: (i) learning of its optimal pricing (resp. allocation) strategy, given its belief regarding its competitors' strategy; (ii) learning the parameters in the price-demand relationship. In equilibrium, each firm seeks to learn the parameters in the price-demand relationship for itself and its competitors, given that prices (resp. quantities) are in equilibrium. In this thesis, we first study the dynamic pricing (resp. allocation) problem when the parameters in the price-demand relationship are known. We then address the dynamic pricing (resp. allocation) problem with learning of the parameters in the price-demand relationship. We show that the problem can be formulated as a bilevel program in disequilibrium and as a Mathematical Program with Equilibrium Constraints (MPECs) in equilibrium. Using results from variational inequalities, bilevel programming and MPECs, we prove that learning the optimal strategies as well as the parameters, is achieved. Furthermore, we design a solution method for efficiently solving the problem. We prove convergence of this method analytically and discuss various insights through a computational study.(cont.) Finally, we consider closed-loop strategies in a duopoly market when demand is stochastic. Unlike open-loop policies (such policies are computed once and for all at the beginning of the time horizon), closed loop policies are computed at each time period, so that the firm can take advantage of having observed the past random disturbances in the market. In a closed-loop setting, subgame perfect equilibrium is the relevant notion of equilibrium. We investigate the existence and uniqueness of a subgame perfect equilibrium strategy, as well as approximations of the problem in order to be able to compute such policies more efficiently.by Carine Simon.Ph.D

    Online spatio - Temporal demand supply matching

    Get PDF

    Internet Traffic Engineering : An Artificial Intelligence Approach

    Get PDF
    Dissertação de Mestrado em Ciência de Computadores, apresentada à Faculdade de Ciências da Universidade do Port
    corecore