A comment on "The selection of preferences through imitation"

We observe that the imitation dynamics of Cubitt and Sugden (Review of Economic Studies, 1998, hereafter CS) is the same as the Replicator Dynamics for a certain class of games. Known results for such games then permit a more complete analysis of the CS imitation process, containing their results as special cases, and extending them considerably. We also offer a comment on the special role of "pure" prospects.Imitation

The Logit-Response Dynamics

We develop a characterization of stochastically stable states for the logit-response learning dynamics in games, with arbitrary specification of revision opportunities. The result allows us to show convergence to the set of Nash equilibria in the class of best-response potential games and the failure of the dynamics to select potential maximizers beyond the class of exact potential games. We also study to which extent equilibrium selection is robust to the specification of revision opportunities. Our techniques can be extended and applied to a wide class of learning dynamics in games.Learning in games, logit-response dynamics, best-response potential games

The Trembling Chairman Paradox

The Chairman Paradox (Farquharson, 1969) is a classical observation in voting games showing that a Chairman endowed with tie-breaking power might end up with her worst outcome. The analysis posits three players whose preferences build a Condorcet cycle and invokes Iterated Elimination of Weakly Dominated Strategies (IEWDS) to select a unique equilibrium. However, IEWDS is a controversial procedure which exhibits well-known weaknesses. This work relies on non-controversial equilibrium refinements instead. For any cardinal payoffs representing the preferences, two pure-strategy equilibria are trembling-hand perfect, the paradoxical one and another one where the Chairman attains her best outcome. The original paradox is restored (and shown not to actually depend on IEWDS) if one considers the stronger concept of proper equilibrium. The analysis casts new light on a classical paradox and illustrates the difference between properness and trembling-hand perfection in a relevant example

Voting under time pressure

In a controlled laboratory experiment we investigate whether time pressure influences voting decisions, and in particular the degree of strategic (insincere) voting. We find that participants under time constraints are more sincere when using the widelyemployed Plurality Voting method. That is, time pressure might reduce strategic voting and hence misrepresentation of preferences. However, there are no effects for Approval Voting, in line with arguments that this method provides no incentives for strategic voting

An axiomatic characterization of Bayesian updating

We provide an axiomatic characterization of Bayesian updating, viewed as a mapping from prior beliefs and new information to posteriors, which is disentangled from any reference to preferences. Bayesian updating is characterized by Non-Innovativeness (events considered impossible in the prior remain impossible in the posterior), Dropping (events contradicted by new evidence are considered impossible in the posterior), and Proportionality (for other events, the posterior simply rescales the prior’s probabilities proportionally). The result clarifies the differences between the normative Bayesian benchmark, alternative models, and actual human behavior

Strength of preference and decisions under risk

Influential economic approaches as random utility models assume a monotonic relation between choice frequencies and “strength of preference,” in line with widespread evidence from the cognitive sciences, which also document an inverse relation to response times. However, for economic decisions under risk, these effects are largely untested, because models used to fit data assume them. Further, the dimension underlying strength of preference remains unclear in economics, with candidates including payoff-irrelevant numerical magnitudes. We provide a systematic, out-of-sample empirical validation of these relations (both for choices and response times) relying on both a new experimental design and simulations

Excess payoff dynamics in games

We present the family of Excess Payoff Dynamics for normal-form games, where the growth of a strategy depends only on its current proportion and the excess payoff, i.e., the payoff advantage of the strategy over the average population payoff. Requiring dependence only on the own excess payoff and a natural sign-preserving condition, the class essentially reduces to aggregate monotonic dynamics, a functional generalization of the Replicator Dynamics. However, Excess Payoff Dynamics also include a different subclass which contains the Replicator Dynamics, the Brown-von Neumann-Nash Dynamics, and other interesting examples as, e.g., satisficing dynamics. We also clarify the relation to excess demand dynamics from microeconomics

Attention and salience in preference reversals

We investigate the implications of Salience Theory for the classical preference reversal phenomenon, where monetary valuations contradict risky choices. It has been stated that one factor behind reversals is that monetary valuations of lotteries are inflated when elicited in isolation, and that they should be reduced if an alternative lottery is present and draws attention. We conducted two preregistered experiments, an online choice study (N=256) and an eye-tracking study (N=64), in which we investigated salience and attention in preference reversals, manipulating salience through the presence or absence of an alternative lottery during evaluations. We find that the alternative lottery draws attention, and that fixations on that lottery influence the evaluation of the target lottery as predicted by Salience Theory. The effect, however, is of a modest magnitude and fails to translate into an effect on preference reversal rates in either experiment. We also use transitions (eye movements) across outcomes of different lotteries to study attention on the states of the world underlying Salience Theory, but we find no evidence that larger salience results in more transitions

The gradual nature of economic errors

Overwhelming evidence from the cognitive sciences shows that, in simple discrimination tasks (determining what is louder, longer, brighter, or even which number is larger) humans make more mistakes and decide more slowly when the stimuli are closer along the relevant scale. We investigate to what extent these effects are relevant for economic decisions in a setting where optimal choices are objectively known (and independent of attitudes toward risk). We find that, even for tasks with objectively-correct answers, error rates and response times increase gradually as expected values become closer. Differences in payoff-independent numerical magnitudes also play a role, which however only becomes clear when one accounts for expected values. We conclude that the gradual effects on choice found in cognitive discrimination paradigms are very much present in economic choices, and depend on economic as well as perceptual variables

Does Backwards Induction Imply Subgame Perfection?

In finite games subgame perfect equilibria are precisely those that are obtained by a backwards induction procedure. In large extensive form games with perfect information this equivalence does not hold: Strategy combinations fulfilling the backwards induction criterion may not be subgame perfect in general. The full equivalence is restored only under additional (topological) assumptions. This equivalence is in the form of a one-shot deviation principle for large games, which requires lower semi-continuous preferences. As corollaries we obtain one-shot deviation principles for particular classes of games, when each player moves only finitely often or when preferences are representable by payoff functions that are continuous at infinity