arXiv subjects

Igal Milchtaich

Publications and source records attributed to Igal Milchtaich.

4 recordsLinked to original sources

arXiv2026

Freemium Model for Information Provision

The paper explores a theoretical freemium model for the sale of information, drawing on mathematical tools used in the study of repeated zero-sum games and Bayesian persuasion. Unlike standard Bayesian persuasion models, the information seller (IS) is indifferent to the actions taken by the information buyer (IB) and is concerned solely with maximizing the revenue from selling information. Offering some information for free may increase the IB's willingness to pay for additional information. The information that the IB seeks is about the state of the world. Initially, the IB only knows the prior distribution over possible states. The IS supplies both free and paid information through signals whose state-dependent distributions determine the IB's posterior via Bayes' rule. The IB's utility is a function of the posterior. An optimal free signal is one that maximizes the IS's expected revenue from the subsequent paid signal. That revenue is equal to the IB's expected utility gain when moving from the posterior induced by the free signal to that induced by the paid signal. The paper characterizes the optimal free and paid signals and derives a formula for the maximal revenue in terms of the IB's utility function. It shows that a revenue gain for the IS from the provision of free information is accompanied by a loss to the IB. Whether free information can increase the IS's revenue depends on the form of the IB's utility function. In the two-state case, that dependence is fully characterized. In the general case, only necessary conditions are obtained. In particular, if the IB's utility function is convex, the IS can never profit from providing free information. This occurs, in particular, when the IB uses the information to solve a decision problem. By contrast, when the IB is engaged in a strategic interaction with a third party, the IS may benefit from providing free information.

econ.TH↗

arXiv2026

Agnostic Sequential Rationality

Agnostic sequential equilibrium (ASE) is a refinement of sequential equilibrium that does not force on the players a single, arbitrary belief system. In addition, whereas sequential equilibrium assumes the players' beliefs to be fully consistent (a notion that is based on perturbations of strategies), ASE employs a novel, simpler and local concept of strong consistency between strategy profiles and off-equilibrium beliefs, which is applicable to a large class of dynamic games, including games with a continuum of actions. In the last respect, the new solution concept is similar to perfect Bayesian equilibrium. It is shown that a strategy profile in an imperfect-information extensive-form game with perfect recall is an ASE precisely when it is a sequential equilibrium with every fully consistent belief system. ASE is generalized by the set-valued solution concept of agnostic sequential polyequilibrium, which allows leaving the players' actions in some information sets partially or completely unspecified.

econ.TH↗

arXiv2026

Potentials and Weak Potentials in Acyclic and Weakly Acyclic Games

In a number of large, important families of finite games, not only is the set of pure-strategy Nash equilibria nonempty but it is also reachable from any initial strategy profile by some sequence of myopic single-player moves to a better or best-reply strategy. This weak acyclicity property is weaker than acyclicity of the game, which requires every such sequence to reach an equilibrium. For example, all perfect-information extensive-form games are weakly acyclic, but they are generally not acyclic as even sequences of best-improvement steps may cycle. Weak acyclicity is equivalent to acyclicity of some priority rule, which is a rule that allows only some improvement moves. It is also equivalent to the existence of a weak potential, which unlike a potential increases along some rather than every sequence as above.

econ.TH↗

arXiv2021

Instability of Defection in the Prisoner's Dilemma Under Best Experienced Payoff Dynamics

We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner`s dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature.

econ.TH↗