Drift effect and timing without observability: experimental evidence

We provide experimental evidence to Binmore and Samuelson’s (1999) insights for modeling the learning process through which equilibrium is selected. They proposed the concept of drift to describe the effect of perturbations on the dynamic process leading to equilibrium in evolutionary games with boundedly rational agents. We test within a random matched population two different versions of the Dalek game where the forward induction equilibrium weakly iterately dominates the other Nash equilibrium in pure strategies. We also assume that the first mover makes her decision first (“timing”) but the second mover is not informed of the first mover's choice (“lack of observability”). Both players are informed of their position in the sequence and of the fact that the second player will decide without knowing the decision of the first player. If the actual observed choices are only those made by other players in previous interactions, the role played by forward induction is replaced with the learning process taking place within the population. Our results support Binmore and Samuelson’s model because the frequency of the forward induction outcome is payoff-sensitive: it strongly increases when we impose a slight change in the payoffs that does not change equilibrium predictions. This evidence reinforces the evolutionary nature of the drift effect.evolutionary games, experiments, drift, forward induction, order of play. J.E.L. Classification: C72, C91

An Experiment on Forward versus Backward Induction: How Fairness and Levels of Reasoning Matter

We report the experimental results on a game with an outside option where induction contradicts with background induction based on a focal, risk dominant equilibrium. The latter procedure yields the equilibrium selected by Harsanyi and Selton's (1888) theory, which is hence here in contradiction with strategic stability (Kohlberg-Mertens (1985)). We find the Harsanyi-Selton solution to be in much better agreement with our data. Since fairness and bounded rationality seem to matter we discuss whether recent behavioral theories, in particular fairness theories and learning, might explain our findings. The fairness theories by Fehr and Schmidt (1999), Bolton and Ockenfels (2000), when calibrated using experimental data on dictator- and ultimatum games, indeed predict that forward induction should play no role for our experiment and that the outside option should be chosen by all sufficiently selfish players. However, there is a multiplicity of "fairness equilibra", some of which seem to be rejected because they require too many levels of reasoning"experiments, equilibrium selection, forward induction, fairness, levels of reasoning.

Forward induction and the excess capacity puzzle: An experimental investigation

While the theoretical industrial organization literature has long argued that excess capacity can be used to deter entry into markets, there is little empirical evidence that incumbent firms effectively behave in this way. Bagwell and Ramey (1996) propose a game with a specific sequence of moves and partially-recoverable capacity costs in which forward induction provides a theoretical rationalization for firm behavior in the field. We conduct an experiment with a game inspired by their work. In our data the incumbent tends to keep the market, in contrast to what the forward induction argument of Bagwell and Ramey would suggest. The results indicate that players perceive that the first mover has an advantage without having to pre-commit capacity. In our game, evolution and learning do not drive out this perception. We back these claims with data analysis, a theoretical framework for dynamics, and simulation results.Entry, excess, capacity, forward induction, equilibrium selection, first-mover advantage, Leex

"Forward induction and the excess capacity puzzle: An experimental investigation"

While the theoretical industrial organization literature has long argued that excess capacity can be used to deter entry into markets, there is little empirical evidence that incumbent firms effectively behave in this way. Bagwell and Ramey (1996) propose a game with a specific sequence of moves and partially-recoverable capacity costs in which forward induction provides a theoretical rationalization for firm behavior in the field. We conduct an experiment with a game inspired by their work. In our data the incumbent tends to keep the market, in contrast to what the forward induction argument of Bagwell and Ramey would suggest. The results indicate that players perceive that the first mover has an advantage without having to pre-commit capacity. In our game, evolution and learning do not drive out this perception. We back these claims with data analysis, a theoretical framework for dynamics, and simulation results.entry, excess capacity, forward induction, equilibrium selection, first-mover advantage

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

Auctions as Coordination Devices

This paper develops an economic argument relating auctions to high market prices. At the core of the argument is the claim that market competition and bidding in an auction should be analyzed as part of one game, where the pricing strategies in the market subgame depend on the bidding strategies during the auction. I show that when there are two licenses for sale the only equilibrium in the overall game that is consistent with the logic of forward induction is the one where firms bid an amount (almost) equal to the profits of the cooperative market outcome and follow a cooperative pricing strategy in the market game resulting in high prices. With three or more licenses the auction format determines whether the forward induction argument works.Auctions, Market prices, Coordination

Pre-Play communication with forgone costly messages: experimental evidence on forward induction

We study communication in a two-player coordination game with Pareto-ranked equilibria. Prior research demonstrates that efficient coordination is difficult without communication but obtains regularly with (mandatory) costless pre-play messages. In a laboratory experiment, we modify communication by making the sending of messages optional and costly. Even small costs dramatically reduce message use, but efficient coordination of actions occurs with similar frequency to that observed under costless communication. Our results can be accounted for by Govindan and Wilson's formalization of forward induction (GW-FI), which selects, among the pure-strategy equilibrium outcomes, the one in which efficiency is achieved without communication. Consistent with the introspective character of GW-FI, the fraction of players who achieve efficient coordination by forgoing the use of reasonably costly optional messages is substantial from the first period, is remarkably stable at that level, and is not significantly affected by learning.Coordination, communication, forward induction, experiment, stag hunt

Forward induction in a wage repeated negotiation

We present a finitely repeated bargaining game with complete information. The stage game is asimultaneous demand game with a fall-back position for both parties, in which we allow one party(say, the union) to estabilish a credible commitment to strike if it is not offered a determinedwage. We try to refine the equilibrium set of the repeated game using a formulation of ForwardInduction. In particular, we say that a path of Nash Equilibria in the repeated game is Consistentwith Forward Induction (CFI) if for all period t the cost of deviation (if it is strictly positive) is greateror equal than the maximal net gain in CFI paths with t-1 horizon. We present several cases in which the average payoff for the union in any CFI path, when thehorizon tends to infinity, is his preferred wage. These results are similar to those obtained with thereputation effects approach and reveal some connection between the FI notion and the approachconsisting of perturbing the game with some incomplete information.Repeated bargaining, forward induction, commitment

An Experiment on Forward versus Backward Induction: How Fairness and Levels of Reasoning Matter

We report the experimental results on a game with an outside option where forward induction contradicts with backward induction based on a focal, risk dominant equilibrium. The latter procedure yields the equilibrium selected by Harsanyi and Selten’s (1988) theory, which is hence here in contradiction with strategic stability (Kohlberg-Mertens (1985)). We find the Harsanyi-Selten solution to be in much better agreement with our data. Since fairness and bounded rationality seem to matter we discuss whether recent behavioral theories, in particular fairness theories and learning, might explain our findings. The fairness theories by Fehr and Schmidt (1999), Bolton and Ockenfels (2000) or Charness and Rabin (2002), when calibrated using experimental data on dictator- and ultimatum games, indeed predict that forward induction should play no role for our experiment and that the outside option should be chosen by all sufficiently selfish players. However, there is a multiplicity of “fairness equilibria”, some of which seem to be rejected because they require too many levels of reasoning. We show that learning theories based on naive priors could alternatively explain our results, but not that of closely related experiments