10,920 research outputs found
What Drives People's Choices in Turn-Taking Games, if not Game-Theoretic Rationality?
In an earlier experiment, participants played a perfect information game
against a computer, which was programmed to deviate often from its backward
induction strategy right at the beginning of the game. Participants knew that
in each game, the computer was nevertheless optimizing against some belief
about the participant's future strategy. In the aggregate, it appeared that
participants applied forward induction. However, cardinal effects seemed to
play a role as well: a number of participants might have been trying to
maximize expected utility.
In order to find out how people really reason in such a game, we designed
centipede-like turn-taking games with new payoff structures in order to make
such cardinal effects less likely. We ran a new experiment with 50
participants, based on marble drop visualizations of these revised payoff
structures. After participants played 48 test games, we asked a number of
questions to gauge the participants' reasoning about their own and the
opponent's strategy at all decision nodes of a sample game. We also checked how
the verbalized strategies fit to the actual choices they made at all their
decision points in the 48 test games.
Even though in the aggregate, participants in the new experiment still tend
to slightly favor the forward induction choice at their first decision node,
their verbalized strategies most often depend on their own attitudes towards
risk and those they assign to the computer opponent, sometimes in addition to
considerations about cooperativeness and competitiveness.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Approachability in unknown games: Online learning meets multi-objective optimization
In the standard setting of approachability there are two players and a target
set. The players play repeatedly a known vector-valued game where the first
player wants to have the average vector-valued payoff converge to the target
set which the other player tries to exclude it from this set. We revisit this
setting in the spirit of online learning and do not assume that the first
player knows the game structure: she receives an arbitrary vector-valued reward
vector at every round. She wishes to approach the smallest ("best") possible
set given the observed average payoffs in hindsight. This extension of the
standard setting has implications even when the original target set is not
approachable and when it is not obvious which expansion of it should be
approached instead. We show that it is impossible, in general, to approach the
best target set in hindsight and propose achievable though ambitious
alternative goals. We further propose a concrete strategy to approach these
goals. Our method does not require projection onto a target set and amounts to
switching between scalar regret minimization algorithms that are performed in
episodes. Applications to global cost minimization and to approachability under
sample path constraints are considered
Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation
We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnoselâskii (1964) and Krasnoselâskii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.Dynamic Programming; Bellman Equation; Unbounded Returns
Uncertainty Aversion and Backward Induction
In the context of the centipede game this paper discusses a solution concept for extensive games that is based on subgame perfection and uncertainty aversion. Players who deviate from the equilibrium path are considered non- rational. Rational players who face non-rational opponents face genuine uncertainty and may have non-additive beliefs about their future play. Rational players are boundedly uncertainty averse and maximise Choquet expected utility. It is shown that if the centipede game is sufficiently long, then the equilibrium strategy is to play `Across' early in the game and to play `Down' late in the game.
Contagion through Learning
We study learning in a large class of complete information normal form games. Players continually face new strategic situations and must form beliefs by extrapolation from similar past situations. We characterize the long-run outcomes of learning in terms of iterated dominance in a related incomplete information game with subjective priors. The use of extrapolations in learning may generate contagion of actions across games even if players learn only from games with payoffs very close to the current ones. Contagion may lead to unique long-run outcomes where multiplicity would occur if players learned through repeatedly playing the same game. The process of contagion through learning is formally related to contagion in global games, although the outcomes generally differ.Similarity, learning, contagion, case-based reasoning, global games, coordination, subjective priors.
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.
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