A cognitive hierarchy model of games

Players in a game are “in equilibrium” if they are rational, and accurately predict other players' strategies. In many experiments, however, players are not in equilibrium. An alternative is “cognitive hierarchy” (CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k − 1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games

Renegotiation Proofness and Climate Agreements: Some Experimental Evidence

The notion of renegotiation-proof equilibrium has become a cornerstone in non-cooperative models of international environmental agreements. Applying this solution concept to the infinitely repeated N-person Prisoners' Dilemma generates predictions that contradict intuition as well as conventional wisdom about public goods provision. This paper reports the results of an experiment designed to test two such predictions. The first is that the higher the cost of making a contribution, the more cooperation will materialize. The second is that the number of cooperators is independent of group size. Although the experiment was designed to replicate the assumptions of the model closely, our results lend very little support to the two predictions.

Legislative bargaining and the dynamics of public investment

We present a legislative bargaining model of the provision of a durable public good over an infinite horizion. In each period, there is a societal endowment which can either be invested in the public good or consumed. We characterize the optimal public policy, defined by the time path of investment and consumption. In each period, a legislature with presentatives of each of n districts bargain over the current period's endowment for investment in the public good and transfers to each district. We analyze the Markov perfect equilibrium under different voting q-rules where q is the number of yes votes required for passage. We show that the efficiency of the public policy is increasing in q because higher q leads to higher investment in the public good and less pork. We examine the theoretical equilibrium predictions by conducting a laboratory experiment with fiveperson committees that compares three alternative voting rules: unanimity (q=5); majority (q=3); and dictatorship (q=1). --dynamic political economy,voting,public goods,bargaining,experiments

Essays on the Impact of Commitment on Bargaining and Efficiency

I study the impact commitment ability has on the efficiency of outcomes in bargaining scenarios and games of coordination. In the first two chapters I analyze the impact of commitment ability on two player bargaining scenarios. In particular, the commitment ability of agents is assumed to be the result of a: revoking) cost which they must pay for backing down from a stated demand. In the first chapter these costs are assumed to be common knowledge and increasing in the magnitude of concession. The agents are shown to benefit from facing higher revoking cost functions. Kalai\u27s Proportional Bargaining Solution is shown to be a good approximation of the equilibrium shares when the cost functions are very high. While all equilibria are efficient in this setting, if the agents are uncertain about these costs when they make their demands the possibility of inefficient equilibria arises. I study this scenario in the second chapter, where the goal is to characterize the set of circumstances that lead to inefficient equilibria. I show that, contrary to models of exogenous commitment, if commitment involves an explicit choice of not backing down, uncertainty regarding revoking costs does not necessarily result in inefficiency: disagreement). If the revoking costs are highly positively correlated across players there can be no disagreement. Even when the revoking costs are independent across players, disagreement cannot arise if the distributions FOSD the uniform distribution. The third chapter considers commitment possibilities in general two player normal form games. Before playing a strategic game, players can commit to not playing some actions at some arbitrarily small cost, progressively shrinking their choice sets. It is shown that if the strategic game is a pure coordination game, the players can avoid all the inefficient Nash Equilibria if they have the ability to commit to not commit. Indeed the unique subgame perfect equilibrium outcome is the Pareto dominant outcome

Competitive Coupon Targeting

With the advent of panel data on household purchase behavior, and the development of statistical procedures to utilize this data, firms can now target coupons to selected households with increasing accuracy and cost effectiveness. As a consequence, new avenues of competition have opened up in which firms play an active role in market segmentation. In this article, we develop an analytical framework to examine the effect of targeting on firm profits, prices, coupon face values, and redemption rates. We also determine firms' optimal mix of offensive and defensive couponing. Among our findings: when rival firms can target their coupon promotions at brand switchers, the outcome will be a prisoner's dilemma in which the net effect of targeting is simply the cost of distribution plus the discount given to redeemers.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100959/1/ECON403.pd

Economic games: An introduction and guide for research

Prosocial behaviors constitute vital ingredients for all types of social interactions and relationships as well as for society at large. Corresponding to this significance, the study of prosocial behaviors has received considerable attention across scientific disciplines. A striking feature of this research is that most disciplines rely on economic games to measure actual prosocial behavior in controlled experimental settings. However, empirical research often fails to fully exploit the richness of this class of paradigms. The current work aims to overcome this issue by providing a theory-driven overview of and introduction to the variety of economic games for researchers in psychology and beyond. Specifically, we introduce prominent theories of games (Game Theory and Interdependence Theory) and show how the concepts from these theories can be integrated in a unifying theoretical framework considering games as providing specific situational affordances for behavior. Additionally, we describe several games in detail, including their structural features, the affordances they involve, the social motives that may guide behavior, the flexibility they entail to manipulate specific situational aspects and, thus, affordances, and typical research findings. We conclude that tailored selection and combination of games and game variants allows to obtain a unique understanding of the underlying psychological processes involved in prosocial behavior. As a practical tool for researchers, we also provide standardized game instructions and guidelines for the implementation of games in future research. Ultimately, the review can foster optimal use of economic games in future work and thereby set the stage for high-class, replicable, and innovative research on human prosociality

Enabling cooperative and negotiated energy exchange in remote communities

Energy poverty at the household level is defined as the lack of access to electricity and reliance on the traditional use of biomass for cooking, and is a serious hindrance to economic and social development. It is estimated that 1.3 billion people live without access to electricity and almost 2.7 billion people rely on biomass for cooking, a majority of whom live in small communities scattered over vast areas of land (mostly in the Sub-Saharan Africa and the developing Asia). Access to electricity is a serious issue as a number of socio-economic factors, from health to education, rely heavily on electricity. Recent initiatives have sought to provide these remote communities with off-grid renewable microgeneration infrastructure such as solar panels, and electric batteries. At present, these resources (i.e., microgeneration and storage) are operated in isolation for individual home needs, which results in an inefficient and costly use of resources, especially in the case of electric batteries which are expensive and have a limited number of charging cycles. We envision that by connecting homes together in a remote community and enabling energy exchange between them, this microgeneration infrastructure can be used more efficiently. Against this background, in this thesis we investigate the methods and processes through which homes in a remote community can exchange energy. We note that remote communities lack general infrastructure such as power supply systems (e.g., the electricity grid) or communication networks (e.g., the internet), that is taken for granted in urban areas. Taking these challenges into account and using insights from knowledge domains such game theory and multi-agent systems, we present two solutions: (i) a cooperative energy exchange solution and (ii) a negotiated energy exchange solution, in order to enable energy exchange in remote communities.Our cooperative energy exchange solution enables connected homes in a remote community to form a coalition and exchange energy. We show that such coalition a results in two surpluses: (i) reduction in the overall battery usage and (ii) reduction in the energy storage losses. Each agents's contribution to the coalition is calculated by its Shapley value or, by its approximated Shapley value in case of large communities. Using real world data, we empirically evaluate our solution to show that energy exchange: (i) can reduce the need for battery charging (by close to 65%) in a community; compared with when they do not exchange energy, and (ii) can improve the efficient use of energy (by up to 10% under certain conditions) compared with no energy exchange. Our negotiated energy exchange solution enables agents to negotiate directly with each other and reach energy exchange agreements. Negotiation over energy exchange is an interdependent multi-issue type of negotiation that is regarded as very difficult and complex. We present a negotiation protocol, named Energy Exchange Protocol (EEP), which simplifies this negotiation by restricting the offers that agents can make to each other. These restrictions are engineered such that agents, negotiation under the EEP, have a strategy profile in subgame perfect Nash equilibrium. We show that our negotiation protocol is tractable, concurrent, scalable and leads to Pareto-optimal outcomes (within restricted the set of offers) in a decentralised manner. Using real world data, we empirically evaluate our protocol and show that, in this instance, a society of agents can: (i) improve the overall utilities by 14% and (ii) reduce their overall use of the batteries by 37%, compared to when they do not exchange energy

Mechanism Design and Analysis Using Simulation-Based Game Models.

As agent technology matures, it becomes easier to envision electronic marketplaces teeming with autonomous agents. Since agents are explicitly programmed to (nearly) optimally compete in these marketplaces, and markets themselves are designed with specific objectives in mind, tools are necessary for systematic analyses of strategic interactions among autonomous agents. While traditional game-theoretic approaches to the analysis of multi-agent systems can provide much insight, they are often inadequate, as they rely heavily on analytic tractability of the problem at hand; however, even mildly realistic models of electronic marketplaces contain enough complexity to render a fully analytic approach hopeless. To address questions not amenable to traditional theoretical approaches, I develop methods that allow systematic computational analysis of game-theoretic models in which the players' payoff functions are represented using simulations (i.e., simulation-based games). I develop a globally convergent algorithm for Nash equilibrium approximation in infinite simulation-based games, which I instantiate in the context of infinite games of incomplete information. Additionally, I use statistical learning techniques to improve the quality of Nash equilibrium approximation based on data collected from a game simulator. I also derive probabilistic confidence bounds and present convergence results about solutions of finite games modeled using simulations. The former allow an analyst to make statistically-founded statements about results based on game-theoretic simulations, while the latter provide formal justification for approximating game-theoretic solutions using simulation experiments. To address the broader mechanism design problem, I introduce an iterative algorithm for search in the design space, which requires a game solver as a subroutine. As a result, I enable computational mechanism design using simulation-based models of games by availing the designer of a set of solution tools geared specifically towards games modeled using simulations. I apply the developed computational techniques to analyze strategic procurement and answer design questions in a supply-chain simulation, as well as to analyze dynamic bidding strategies in sponsored search auctions. Indeed, the techniques I develop have broad potential applicability beyond electronic marketplaces: they are geared towards any system that features competing strategic players who respond to incentives in a way that can be reasonably predicted via a game-theoretic analysis.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60786/1/yvorobey_1.pd

Competition with list prices

Retail prices in stores are often lower than widely advertised list prices. We study the competitive role of such list prices in a homogeneous product duopoly where firms first set list prices before setting possibly reduced retail prices. Building on Varian (1980), we assume that some consumers observe no prices, some observe all prices, and some only observe the more salient list prices. We show that when the latter group chooses myopically, firms' ability to use list prices lowers average transaction prices. This effect is weakened when these consumers are rational. The possibility to use list prices facilitates collusion.</p