The strategic behavior of rational novices

There is a growing amount of experimental evidence that suggests people often deviate from the predictions of game theory. Some scholars attempt to explain the observations by introducing errors into behavioral models. However, most of these modifications are situation dependent and do not generalize. A new theory, called the rational novice model, is introduced as an attempt to provide a general theory that takes account of erroneous behavior. The rational novice model is based on two central principals. The first is that people systematically make inaccurate guesses when they are evaluating their options in a game-like situation. The second is that people treat their decisions similar to a portfolio problem. As a result, non optimal actions in a game theoretic sense may be included in the rational novice strategy profile with positive weights.

The rational novice model can be divided into two parts: the behavioral model and the equilibrium concept. In a theoretical chapter, the mathematics of the behavioral model and the equilibrium concept are introduced. The existence of the equilibrium is established. In addition, the Nash equilibrium is shown to be a special case of the rational novice equilibrium. In another chapter, the rational novice model is applied to a voluntary contribution game. Numerical methods were used to obtain the solution. The model is estimated with data obtained from the Palfrey and Prisbrey experimental study of the voluntary contribution game. It is found that the rational novice model explains the data better than the Nash model. Although a formal statistical test was not used, pseudo R^2 analysis indicates that the rational novice model is better than a Probit model similar to the one used in the Palfrey and Prisbrey study.

The rational novice model is also applied to a first price sealed bid auction. Again, computing techniques were used to obtain a numerical solution. The data obtained from the Chen and Plott study were used to estimate the model. The rational novice model outperforms the CRRAM, the primary Nash model studied in the Chen and Plott study. However, the rational novice model is not the best amongst all models. A sophisticated rule-of-thumb, called the SOPAM, offers the best explanation of the data.

Characterizing distribution rules for cost sharing games

In noncooperative cost sharing games, individually strategic agents choose resources based on how the welfare (cost or revenue) generated at each resource (which depends on the set of agents that choose the resource) is distributed. The focus is on finding distribution rules that lead to stable allocations, which is formalized by the concept of Nash equilibrium, e.g., Shapley value (budget-balanced) and marginal contribution (not budget-balanced) rules.

Recent work that seeks to characterize the space of all such rules shows that the only budget-balanced distribution rules that guarantee equilibrium existence in all welfare sharing games are generalized weighted Shapley values (GWSVs), by exhibiting a specific 'worst-case' welfare function which requires that GWSV rules be used. Our work provides an exact characterization of the space of distribution rules (not necessarily budget-balanced) for any specific local welfare functions remains, for a general class of scalable and separable games with well-known applications, e.g., facility location, routing, network formation, and coverage games.

We show that all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to GWSV rules on some 'ground' welfare functions. Therefore, it is neither the existence of some worst-case welfare function, nor the restriction of budget-balance, which limits the design to GWSVs. Also, in order to guarantee equilibrium existence, it is necessary to work within the class of potential games, since GWSVs result in (weighted) potential games.

We also provide an alternative characterization—all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to generalized weighted marginal contribution (GWMC) rules on some 'ground' welfare functions. This result is due to a deeper fundamental connection between Shapley values and marginal contributions that our proofs expose—they are equivalent given a transformation connecting their ground welfare functions. (This connection leads to novel closed-form expressions for the GWSV potential function.) Since GWMCs are more tractable than GWSVs, a designer can tradeoff budget-balance with computational tractability in deciding which rule to implement.

Motor coordination: when two have to act as one.

Trying to pass someone walking toward you in a narrow corridor is a familiar example of a two-person motor game that requires coordination. In this study, we investigate coordination in sensorimotor tasks that correspond to classic coordination games with multiple Nash equilibria, such as "choosing sides," "stag hunt," "chicken," and "battle of sexes". In these tasks, subjects made reaching movements reflecting their continuously evolving "decisions" while they received a continuous payoff in the form of a resistive force counteracting their movements. Successful coordination required two subjects to "choose" the same Nash equilibrium in this force-payoff landscape within a single reach. We found that on the majority of trials coordination was achieved. Compared to the proportion of trials in which miscoordination occurred, successful coordination was characterized by several distinct features: an increased mutual information between the players' movement endpoints, an increased joint entropy during the movements, and by differences in the timing of the players' responses. Moreover, we found that the probability of successful coordination depends on the players' initial distance from the Nash equilibria. Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times.

多对一供应链零售商驱动型收入共享契约下的生产决策

针对多对一供应链结构中零售商具有较强议价能力的特点,建立了零售商为主方、制造商为从方的Stackelberg主从对策模型;给出在零售商提供契约条款的对称博弈中,制造商生产产品策略存在唯一最优解的证明;分析了零售商契约参数变量的决策问题;讨论了收入共享契约下分散供应链同集中供应链决策的关系.通过仿真实验,分析验证了契约参数及产品的可替代性对供应链绩效的影响。

Collocation Games and Their Application to Distributed Resource Management

We introduce Collocation Games as the basis of a general framework for modeling, analyzing, and facilitating the interactions between the various stakeholders in distributed systems in general, and in cloud computing environments in particular. Cloud computing enables fixed-capacity (processing, communication, and storage) resources to be offered by infrastructure providers as commodities for sale at a fixed cost in an open marketplace to independent, rational parties (players) interested in setting up their own applications over the Internet. Virtualization technologies enable the partitioning of such fixed-capacity resources so as to allow each player to dynamically acquire appropriate fractions of the resources for unencumbered use. In such a paradigm, the resource management problem reduces to that of partitioning the entire set of applications (players) into subsets, each of which is assigned to fixed-capacity cloud resources. If the infrastructure and the various applications are under a single administrative domain, this partitioning reduces to an optimization problem whose objective is to minimize the overall deployment cost. In a marketplace, in which the infrastructure provider is interested in maximizing its own profit, and in which each player is interested in minimizing its own cost, it should be evident that a global optimization is precisely the wrong framework. Rather, in this paper we use a game-theoretic framework in which the assignment of players to fixed-capacity resources is the outcome of a strategic "Collocation Game". Although we show that determining the existence of an equilibrium for collocation games in general is NP-hard, we present a number of simplified, practically-motivated variants of the collocation game for which we establish convergence to a Nash Equilibrium, and for which we derive convergence and price of anarchy bounds. In addition to these analytical results, we present an experimental evaluation of implementations of some of these variants for cloud infrastructures consisting of a collection of multidimensional resources of homogeneous or heterogeneous capacities. Experimental results using trace-driven simulations and synthetically generated datasets corroborate our analytical results and also illustrate how collocation games offer a feasible distributed resource management alternative for autonomic/self-organizing systems, in which the adoption of a global optimization approach (centralized or distributed) would be neither practical nor justifiable.

Effect of Selfish Node Behavior on Efficient Topology Design

The problem of topology control is to assign per-node transmission power such that the resulting topology is energy efficient and satisfies certain global properties such as connectivity. The conventional approach to achieve these objectives is based on the fundamental assumption that nodes are socially responsible. We examine the following question: if nodes behave in a selfish manner, how does it impact the overall connectivity and energy consumption in the resulting topologies? We pose the above problem as a noncooperative game and use game-theoretic analysis to address it. We study Nash equilibrium properties of the topology control game and evaluate the efficiency of the induced topology when nodes employ a greedy best response algorithm. We show that even when the nodes have complete information about the network, the steady-state topologies are suboptimal. We propose a modified algorithm based on a better response dynamic and show that this algorithm is guaranteed to converge to energy-efficient and connected topologies. Moreover, the node transmit power levels are more evenly distributed, and the network performance is comparable to that obtained from centralized algorithms.

Partial Cooperative Equilibria: Existence and Characterization

We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria exist in supermodular games. Finally, we provide an application to strategic network formation where such solution concepts may be useful.

Coordination, Efficiency and Two-Sided Cheap Talk

We consider the Battle of the Sexes game with incomplete information and allow two-sided cheap talk before the game is played. We characterise the set of fully revealing symmetric cheap talk equilibria. The best fully revealing symmetric cheap talk equilibrium, when exists, has a desirable characteristic. When the players' types are different, it fully coordinates on the ex-post efficient pure Nash equilibrium. We also analyse the mediated communication equilibria of the game. We find the range of the prior for which this desirable equilibrium exists under unmediated and mediated communication processes.

Ambiguity, social opinion and the use of common property resources

In this paper we argue that ambiguity, combined with social opinion formation, can be used as the foundation of a game-theoretic equilibrium concept that transcends the standard Nash equilibrium concept, applied to a model of the tragedy of the commons. Our approach sheds light on the international environmental crisis and the relevant ongoing international negotiations. We conclude that social opinion formation in most cases has a significant impact on equilibrium common property resource usage.

Strategic behavior under partial cooperation

We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash's best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both types of equilibria. We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return.

Stressed Web Environments as Strategic Games: Risk Profiles and Weltanschauung

We consider the behaviour of a set of services in a stressed web environment where performance patterns may be difficult to predict. In stressed environments the performances of some providers may degrade while the performances of others, with elastic resources, may improve. The allocation of web-based providers to users (brokering) is modelled by a strategic non-cooperative angel-daemon game with risk profiles. A risk profile specifies a bound on the number of unreliable service providers within an environment without identifying the names of these providers. Risk profiles offer a means of analysing the behaviour of broker agents which allocate service providers to users. A Nash equilibrium is a fixed point of such a game in which no user can locally improve their choice of provider – thus, a Nash equilibrium is a viable solution to the provider/user allocation problem. Angel daemon games provide a means of reasoning about stressed environments and offer the possibility of designing brokers using risk profiles and Nash equilibria.

Implementing efficient graphs in connection networks

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first property, Pareto Nash implementation (PNI), requires that the efficient outcome always be implemented in a Nash equilibrium and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism and other asymmetric variations are the only mechanisms that meet PNI. These mechanisms are also characterized under strong Nash implementation. The second property, weakly Pareto Nash implementation (WPNI), requires that the least inefficient equilibrium Pareto dominates any other equilibrium. The egalitarian mechanism (EG) and other asymmetric variations are the only mechanisms that meet WPNI and individual
rationality. EG minimizes the price of stability across all individually rational mechanisms. © Springer-Verlag Berlin Heidelberg 2012

Key Players and Key Groups in Teams

This paper contributes to the literature on centrality measures in economics by defining a team game and identifying the key players and key groups
in the game. We extend the work of Ballester et al. (Econometrica, 2006) by incorporating a network outcome component in the players' payoff functions and prove that there is a unique interior Nash Equilibrium in pure strategies. We develop a team intercentrality measure based on alternative scenarios that capture the externality created by teammates on each player.

Partial Cooperation in Strategic Decision Situations

We consider a normal form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. These collective actions typically represent a certain number of dimensions in the players’ strategy space. The actions represented by the other dimensions of the strategy space remain under the complete, individual control of the players.
We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are developed for these new equilibrium concepts. We identify conditions on these partial cooperative games under which the various equilibrium concepts are equivalent.
We apply this game theoretic framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly typically a merger paradox emerges in the partial cooperative equilibrium, which vanishes if the cartel of collaborators exploits its leadership position. Our application to international pollution abatement treaties shows that cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.

Stochastic short-term maintenance scheduling of GENCOs in an oligopolistic electricity market

In the proposed model, the independent system operator (ISO) provides the opportunity for maintenance outage rescheduling of generating units before each short-term (ST) time interval. Long-term (LT) scheduling for 1 or 2 years in advance is essential for the ISO and the generation companies (GENCOs) to decide their LT strategies; however, it is not possible to be exactly followed and requires slight adjustments. The Cournot-Nash equilibrium is used to characterize the decision-making procedure of an individual GENCO for ST intervals considering the effective coordination with LT plans. Random inputs, such as parameters of the demand function of loads, hourly demand during the following ST time interval and the expected generation pattern of the rivals, are included as scenarios in the stochastic mixed integer program defined to model the payoff-maximizing objective of a GENCO. Scenario reduction algorithms are used to deal with the computational burden. Two reliability test systems were chosen to illustrate the effectiveness of the proposed model for the ST decision-making process for future planned outages from the point of view of a GENCO.