Cognition and framing in sequential bargaining for gains and losses

Noncooperative game-theoretic models of sequential bargaining give an underpinning to cooperative solution concepts derived from axioms, and have proved useful in applications (see Osborne and Rubinstein 1990). But experimental studies of sequential bargaining with discounting have generally found systematic deviations between the offers people make and perfect equilibrium offers derived from backward induction (e.g., Ochs and Roth 1989). We have extended this experimental literature in two ways. First, we used a novel software system to record the information subjects looked at while they bargained. Measuring patterns of information search helped us draw inferences about how people think, testing as directly as possible whether people use backward induction to compute offers. Second, we compared bargaining over gains that shrink over time (because of discounting) to equivalent bargaining over losses that expand over time. In the games we studied, two players bargain by making a finite number of alternating offers. A unique subgame-perfect equilibrium can be computed by backward induction. The induction begins in the last period and works forward. Our experiments use a three-round game with a pie of $5.00 and a 50-percent discount factor (so the pie shrinks to$2.50 and $1.25 in the second and third rounds). In the perfect equilibrium the first player offers the second player$1.25 and keeps $3.75

Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining

We did experiments in a three-round bargaining game where the (perfect) equilibrium offer was $1.25 and an equal split was$2.50. The average offer was $2.11. Patterns of information search (measured with a computerized information display) show limited lookahead rather than backward induction. Equilibrium theories which adjust for social utilities (reflecting inequality-aversion or reciprocity) cannot explain the results because they predict subjects will make equilibrium offers to “robot” players, but offers to robots are only a little lower. When trained subjects (who quickly learned to do backward induction) bargained with untrained subjects, offers ended up halfway between equilibrium and$2.11

Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining

We ran three-round sequential bargaining experiments in which the perfect equilibrium offer was $1.25 and an equal split was$2.50. Subjects offered $2.11 to other subjects,$1.84 to “robot” players (who are known to play subgame perfectly), and $1.22 to robots after instruction in backward induction. Measures of information search showed that subjects did not look at the amounts being divided in different rounds in the correct order, and for the length of time, necessary for backward induction, unless they were specifically instructed. The results suggest that most of the departure from perfect equilibrium is due to limited computation and some is due to fairness

Competitive signaling and bluffing: An empirical and normative investigation

Competitive signals are actions by competitors that provide indications of their intentions. Such signals may either be truthful indications of competitor\u27s intentions, or bluffs, designed to mislead competitors to benefit the sender. This research focuses on competitive signaling interactions involving bluffing, and tries to answer the following questions: (1) to what extent do firms send bluff signals in competitive environments?; (2) what are the characteristics of bluff signals and their senders?; (3) what are the perceived characteristics of bluff signals and their senders from the receiving manager\u27s point of view?; (4) are some managers better interpreters of competitive signals than others; what are the characteristics of such managers?; (5) how do senders and receivers interact strategically? I address these questions by conducting four related studies: In the first study, the focus is on the signal sender. In a survey of executives across product categories, I test whether firms send bluffs, and the characteristics of bluff signals and their senders. Given the sensitive nature of the topic, a statistical technique for the study of unacceptable behavior, the Randomized Response Technique, is used for data collection. Building on the results of the first study, I focus on the signal receiver in the second and third studies. Two measurement approaches are used for studying signal interpretation. In the second study, managers\u27 perceptions of competitive signals are estimated using Conjoint Analysis. In the third study, the Theory of Signal Detection is used for testing managers\u27 discrimination ability and interpretation accuracy. The stimuli for both studies are designed based on findings from the first study, and hypotheses concerning receiver characteristics as independent variables affecting signal interpretation are tested. Finally, in a fourth study, the competitive signaling interaction is analyzed using a game theoretic framework. Results from the empirical studies are incorporated into the analysis. Different strategies for both players, sender and receiver, are examined to provide normative implications for competitive signaling interactions involving bluffing