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A challenge associated with fisheries management is when there are many potential participants, and each participant has virtually zero effect (small agents), but their collective action may be significant. Individual quotas or effort restrictions may not be well suited in such cases. For the abovementioned problem, we explore the mean field games (MFGs) framework, which considers non‐cooperative games of infinitely many agents. The MFGs approach allows considering progressive costs and taxes, which would be difficult or impossible to consider otherwise, and the influence of uncertainties in agents' decisions on their aggregate action. The mean field games are applied to model a fishery with many small fishing firms, which are more or less identical, and to analyze the implications of different management policies on their economic performance and resource sustainability. The main focus is on financial regulations, which make the excessive effort unprofitable.

We expand the scope of the two-aggregate method by applying it to a situation in which many heterogeneous players are free to contribute to both aggregates. Such situations naturally arise in various resource allocation problems. Hence, our method is useful in many applications. A production-appropriation model is employed to illustrate how the problem of establishing the Nash equilibrium can be reduced from solving n > 2 best-response functions in n unknowns to solving two consistency conditions in two unknowns. We then conduct a comparative static exercise that the conventional approach could not handle easily, if at all, to demonstrate the power of our method.

In this paper, we consider a sequential allocation problem with n individuals. The first individual can consume any amount of a resource, leaving the remainder for the second individual, and so on. Motivated by the limitations associated with the cooperative or non-cooperative solutions, we propose a new approach from basic definitions of representativeness and equal treatment. The result is a unique asymptotic allocation rule for any number of individuals. We show that it satisfies a set of desirable properties.

The digital transition is a challenge that developed countries are currently facing. The transition process is associated with different degrees of uncertainty, which are particularly relevant for changes that have to do with the provision of goods and services produced by public administrations. Our paper uses a partial equilibrium model to study the effects of uncertainty on the public provision of goods and services produced by bureaucratic agencies, including the incentive of the government to consolidate production. We assume that bureaucratic agencies may play either a cooperative game with each other and a non-cooperative game against the government (i.e., a consolidated bureaucracy) or a non-cooperative game with each other and against the government (i.e., competing bureaus). Both the government and the bureaus face tradeoffs between maximizing the electorate preferences and extracting some political and/or bureaucratic rents. We find that a cooperative (competitive) bureaucratic solution depends on the nature of the goods produced. We find that costs’ uncertainty affects the level of public production and the way the policymakers extract their rents.

Currently, highly complex supply networks are vulnerable to various kinds of disruptions, which may greatly affect the operational efficiency of supply chains. This calls for the development of management approaches to build a resilient supply chain under disruptions. In this work, we are mainly interested in transportation disruptions that affect shipments along a supply chain and study the decision problem of suppliers in regards to acquiring and sharing transportation disruption information in a competitive setting. In particular, we investigate a two-echelon supply chain consisting of one buyer and two competing suppliers where the buyer places an order for a single product with the two suppliers. During the product transportation process, a disruption may occur and damage the shipments in transit. In the face of such a transportation disruption, each supplier can either have its shipment inspected and reveal information to the buyer or continue without taking any action. We study this problem by formulating it as a non-cooperative game and derive equilibrium results for the two suppliers on whether or not to share information considering competition. We find that the timing and severity of the transportation disruption affect a supplier’s decision on whether to acquire and share private information. By adopting an incentive mechanism, the buyer can raise the probability that a supplier shares its information, which could eventually enhance the performance of the disrupted supply chain. The supplier in a stronger market position usually acts passively towards the disruption, while the competing supplier tends to use information sharing as a way to win market share from its competitor. In addition, a sensitivity analysis is conducted on some important parameters of our model to show the impact of information sharing on supply chain performance.

In this paper, we propose non-model-based strategies for locally stable convergence to Nash equilibrium in quadratic noncooperative games where acquisition of information (of two different types) incurs delays. Two sets of results are introduced: (a) one, which we call cooperative scenario, where each player employs the knowledge of the functional form of his payoff and knowledge of other players’ actions, but with delays; and (b) the second one, which we term the noncooperative scenario, where the players have access only to their own payoff values, again with delay. Both approaches are based on the extremum seeking perspective, which has previously been reported for real-time optimization problems by exploring sinusoidal excitation signals to estimate the Gradient (first derivative) and Hessian (second derivative) of unknown quadratic functions. In order to compensate distinct delays in the inputs of the players, we have employed predictor feedback. We apply a small-gain analysis as well as averaging theory in infinite dimensions, due to the infinite-dimensional state of the time delays, in order to obtain local convergence results for the unknown quadratic payoffs to a small neighborhood of the Nash equilibrium. We quantify the size of these residual sets and corroborate the theoretical results numerically on an example of a two-player game with delays.

This paper formally introduces and studies a non-cooperative multi-agent game under uncertainty. The well-known Nash equilibrium is employed as the solution concept of the game. While there are several formulations of a stochastic Nash equilibrium problem, we focus mainly on a two-stage setting of the game wherein each agent is risk-averse and solves a rival-parameterized stochastic program with quadratic recourse. In such a game, each agent takes deterministic actions in the first stage and recourse decisions in the second stage after the uncertainty is realized. Each agent’s overall objective consists of a deterministic first-stage component plus a second-stage mean-risk component defined by a coherent risk measure describing the agent’s risk aversion. We direct our analysis towards a broad class of quantile-based risk measures and linear-quadratic recourse functions. For this class of non-cooperative games under uncertainty, the agents’ objective functions can be shown to be convex in their own decision variables, provided that the deterministic component of these functions have the same convexity property. Nevertheless, due to the non-differentiability of the recourse functions, the agents’ objective functions are at best directionally differentiable. Such non-differentiability creates multiple challenges for the analysis and solution of the game, two principal ones being: (1) a stochastic multi-valued variational inequality is needed to characterize a Nash equilibrium, provided that the players’ optimization problems are convex; (2) one needs to be careful in the design of algorithms that require differentiability of the objectives. Moreover, the resulting (multi-valued) variational formulation cannot be expected to be of the monotone type in general. The main contributions of this paper are as follows: (a) Prior to addressing the main problem of the paper, we summarize several approaches that have existed in the literature to deal with uncertainty in a non-cooperative game. (b) We introduce a unified formulation of the two-stage SNEP with risk-averse players and convex quadratic recourse functions and highlight the technical challenges in dealing with this game. (c) To handle the lack of smoothness, we propose smoothing schemes and regularization that lead to differentiable approximations. (d) To deal with non-monotonicity, we impose a generalized diagonal dominance condition on the players’ smoothed objective functions that facilitates the application and ensures the convergence of an iterative best-response scheme. (e) To handle the expectation operator, we rely on known methods in stochastic programming that include sampling and approximation. (f) We provide convergence results for various versions of the best-response scheme, particularly for the case of private recourse functions. Overall, this paper lays the foundation for future research into the class of SNEPs that provides a constructive paradigm for modeling and solving competitive decision making problems with risk-averse players facing uncertainty; this paradigm is very much at an infancy stage of research and requires extensive treatment in order to meet its broad applications in many engineering and economics domains.

The article illustrates distinctions between important concepts of game theory, which support understanding the relation between subjects on competitive and regulated telecommunications services market. Especially it shows that often used distinction between retail and wholesale market that treat them respectively as competitive and cooperative can be misleading or even wrong

In resource contribution games, a class of non-cooperative games, the players want to obtain a bundle of resources and are endowed with bags of bundles of resources that they can make available into a common for all to enjoy. Available resources can then be used towards their private goals. A player is potentially satisfied with a profile of contributed resources when his bundle could be extracted from the contributed resources. Resource contention occurs when the players who are potentially satisfied, cannot actually all obtain their bundle. The player’s preferences are always single-minded (they consider a profile good or they do not) and parsimonious (between two profiles that are equally good, they prefer the profile where they contribute less). What makes a profile of contributed resources good for a player depends on their attitude towards resource contention. We study the problem of deciding whether an outcome is a pure Nash equilibrium for three kinds of players’ attitudes towards resource contention: public contention-aversity, private contention-aversity, and contention-tolerance. In particular, we demonstrate that in the general case when the players are contention-averse, then the problem is harder than when they are contention-tolerant. We then identify a natural class of games where, in presence of contention-averse preferences, it becomes tractable, and where there is always a Nash equilibrium.

This paper is concerned with the distributed Nash equilibrium (NE) computation problem for non-cooperative games subject to partial-decision information. For the purpose of congestion mitigation, coding-decoding-based schemes are constructed on the basis of logarithmic and uniform quantizers, respectively. To be specific, the data (decision variable) are first mapped to codewords by an encoder scheme, and then sent to the neighboring agents through a directed communication network (with non-doubly stochastic weighted matrix). By using a decoder scheme, a new distributed algorithm is established for seeking the NE. In order to eliminate the convergence error caused by quantization, a dynamic variable is introduced and a modified coding-decoding-based algorithm is constructed under the uniform quantization scheme, which ensures the asymptotic convergence to the NE. The proposed algorithm only requires that the weighted adjacency matrix is row stochastic instead of double stochastic. Finally, one numerical example is provided to validate the effectiveness of our algorithms.