The ethnologist, Diamond Jenness, who was asked by the Canadian government in 1913 to join Stefansson's Arctic expedition to study Eskimos for three years, records the following in his diary:

Noncooperative, nonrepeated game theory is about strangers with no shared history, like the residents of Jenness' “great city.”They meet, interact strategically in their individual self interests according to well specified rules and payoffs, and never meet again.These stark conditions are necessary to ensure that the noncooperative, nonrepeated game theoretic prediction for the interaction is not part of a sequence with a past and a future.Thus, repeated games are analyzed differently because now strangers can potentially cooperate by developing their own history and future.

Theorists have long studied the fundamental problem that cooperative, socially efficient outcomes generally cannot be supported as equilibria in finite games. The puzzle is the occurrence of cooperative behavior in the absence of immediate incentives to engage in such behavior. For example, in two-person bargaining experiments, where noncooperative behavior does not support efficient outcomes, we observe more cooperative behavior and greater efficiency than such environments are expected to produce. Similarly, in public good experiments with group size varying from 4 to 100, people tend to achieve much higher payoff levels than predicted by noncooperative theory. Moreover, examples of the achievement of cooperative behavior by decentralized means have a long history in the human experience. Anthropological and archeological evidence suggests that sharing behavior is ubiquitous in tribal cultures that lack markets,monetary systems, or other means of storing and redistributing wealth (see, e.g., Cosmides and Tooby, 1987, 1989; Isaac, 1978; Kaplan and Hill, 1985b; Tooby and De Vore, 1987; Trivers, 1971).

In this paper we draw together theoretical and experimental evidence from game theory, evolutionary psychology, and experimental economics that provides the basis for developing a reciprocity framework for understanding the persistence of cooperative outcomes in the face of contrary individual incentives. Repeated game theory with discounting or infinite time horizons allows for cooperative solutions but does not yield conditions for predicting them (Fudenberg and Tirole, 1993). Recent research in evolutionary psychology (Cosmides and Tooby, 1987, 1989, 1992) suggests that humans may be evolutionarily predisposed to engage in social exchange using mental algorithms that identify and punish cheaters.

We use variations on a relatively transparent, two-person extensive form bargaining game to examine principles of self-evident play (Kreps, 1990a) using experimental analysis. Our game is transparent if players can be expected to understand the relationship between the possible sequences of plays with their counterparts and the resulting payoffs that can be achieved. However, how to develop strategy for a relatively transparent game may not be self-evident because it requires players to be confident about their counterparts' actions and reactions. So, when are players likely to be mutually confident?

Evolutionary psychology provides one approach to answering this question. Hoffman et al. (1996b) and the references therein give a more extended discussion of the role of evolutionary psychology in explaining many economics experiments that exhibit anomalous behavior relative to standard theory. Even though economic theory assumes that individuals employ general purpose consciously cognitive algorithms to optimize gains in any situation, evolutionary psychology assumes that individuals deploy domain-specific cognitive algorithms, with different algorithms being used for different situations, often in nonconscious ways. Economic theory disciplines our thinking by requiring behaviors that maximize individual utility, whereas evolutionary psychology disciplines our thinking by requiring blue-prints for behavioral activity that can be adapted under natural selection. Of course the relative value of these blueprints from nature depends on their subsequent development by cultural interaction (nurture) and a continuing evaluation of behavioral success through experience.

In this chapter, we address the following question: Can we use principles from game theory, experimental economics, and evolutionary psychology to better understand what is self-evident to players playing our extensive form games?

I. Principles of Behavior

The fundamental principles which underpin the propositions we examine experimentally can be stated as follows:…

In this chapter, we ask if instructional and procedural manipulation can be used in a systematic way to understand the social norms that have been said to be the cause of deviations from game theoretic predictions in dictator and other games. We find that such manipulations, intended to affect subjects' degree of social distance from the experimenter and assumed to affect expectations of reciprocity, play a key role in determining and understanding behavior.

Dictator games with and without monetary rewards have been compared by Forsythe et al. (1994; hereafter FHSS). In this game, a subject and his or her anonymous counterpart in another room “has been provisionally allocated” $10. The subject's task is to decide how to “divide” the $10; the counterpart has no recourse but must accept the allocation. These phrases appearing in quotation marks constitute the exact language that appears in the instructions to the subjects. As we shall see, this language is not entirely benign. It was first used by Kahneman et al. (1986, pp. 105–6; hereafter KKT); and FHSS desired to stay close to this originating study to examine its replicability and the effect of reward variations in this version of the game.

Dictator games are an interesting vehicle for studying the meaning and interpretation of fairness. The dictator game controls for strategic behavior in the ultimatum game where the fairness interpretation first emerged prominently. In the ultimatum game, player 1 offers any amount of the $10 to player 2. If player 2 accepts, the $10 is divided according to the terms of the offer; if player 2 rejects, each player gets 0.

Joyce (1984) reports the results of experiments with a Walrasian tâtonnement auction that show that the mechanism is stable, exhibits strong convergence properties, and generates efficiencies that average better than 97%. He also found that when subjects could see part of the order flow (excess demand), prices tended to be lower. His experiments consisted of a stationary environment where subjects were provided single unit supply and demand functions.We assess the robustness of his results in a more general multiunit per subject setting; and we systematically investigate the effect of various rules about order flow information and message restriction rules on the performance of the Walrasian mechanism.

Our experiments are motivated by several considerations.

1. When there are both buyers and sellers in the market, each of which has one unit to buy or sell, the only Nash equilibria of the Walrasian tâtonnement mechanism are those that support the competitive equilibrium outcome. Furthermore, a Walrasian tâtonnement process can be designed that has a dominant strategy equilibrium where each participant reveals value or cost (see McAfee, 1992). The design imposes constraints on participant messages; specifically, at the announced price at t, if excess demand is positive (negative), any seller (buyer) not registering a sell (buy) order at t cannot register an order at time t + 1. Without this improvement rule, the dominant strategy equilibrium outcome no longer exists.But even with this improvement rule, the dominant strategy revelation property does not hold when demands and supplies are multiunit, since a participant may influence price without being entirely out of the market.

In an ultimatum game, player 1 makes an offer of $X from a total of $M to player 2. If player 2 accepts the offer, then player 1 is paid $(M − X) and player 2 receives $X; if player 2 rejects the offer, each gets zero. In the ultimatum game experiments reported in the literature, M is typically not more than $10 (see Forsythe et al., 1994, hereafter FHSS; Hoffman et al., 1994, hereafter HMSS, and the literature cited therein). We report new results for 50 bargaining pairs in which M = $100 and compare them with previous outcomes from 48 pairs with M = $10. The need for an examination of the effect of increased stakes on ultimatum bargaining is suggested by a literature survey of the effect of varying the stakes in a wide variety of decision-making and market experiments over the last 33 years (Smith and Walker, 1993b). Many cases were found in which the predictions of theory were improved when the monetary rewards were increased.There were also cases in which the level of monetary rewards had no effect on the results. Consequently, it is necessary to examine the stakes question on a case-by-case basis. The previously reported effect of instructional changes, which define different institutional contexts, on ultimatum game outcomes, and the effect of stakes reported here, suggest a game formulation that explains changes in the behavior of both players as a result of changes in the instructional treatments. We formulated such a model and indicate how it might be further tested.

I. Theory and Previous Results

Suppose the payoffs and individual rationality of the players are common knowledge.

Introduction

To what degree do individual decision biases affect aggregate behavior? This question was introduced, and “answered, ” in the accounting literature twenty years ago when Gonedes and Dopuch (1974) argued that market efficiency necessarily precluded any impact of individual bias on aggregate capital–market behavior (that is, price). We know now that this claim need not be true. Recent advances in both theoretical and empirical research open the door for the influence of individual bias on aggregate–level behavior in capital markets as well as other aggregate settings. Experimental methods enhance our ability to pinpoint when biases do occur, measure the cost of bias, and examine what factors extinguish biases. In this chapter, we review the historical development of the issue of individual and aggregate behavior and develop a framework to systematically advance our knowledge in this area.

Since no generally accepted theory linking individual behavior to aggregate level behavior exists, we develop a framework enumerating the observable factors that distinguish individual decision–making settings from aggregate decision–making settings. Since these factors transcend theoretical paradigms, they form the basis for dialog between those that draw theory from economics and those that draw theory from psychology. In the spirit of enhancing such a dialog, we use this framework to examine several streams of research, and begin to address how changes in observable factors affect aggregate behavior.

In examining these settings, we ask not only whether individual biases persist at the aggregate level, but also whether aggregate settings introduce “new” biases of their own.

As a consequence of technological economies of scale in pipeline transportation, natural gas has been considered a classic case of natural monopoly. But entry, growth and development in the industry in the United States has yielded more than one pipeline in most producing fields. Similarly most wholesale markets are served by at least two pipelines [Norman (1987)]. The concept of natural monopoly is a static concept; i.e. given any level of demand, declining long run marginal planning cost implies that one pipeline - a very large one, if demand is high – yields the least-cost solution to satisfying that demand. But in fact demand is cyclical and tends to grow over time, and new gas wells and gas fields develop over time.