Itai Sher

Credibility and determinism in a game of persuasion

This paper studies a game of persuasion. A speaker attempts to persuade a listener to take an action by presenting evidence. Glazer and Rubinstein (2006) showed that when the listeners decision is binary, neither randomization nor commitment have any value for the listener, and commented that the binary nature of the decision was important for the commitment result. In this paper, I show that concavity is the critical assumption for both results: no value to commitment and no value to randomization. Specifically, the key assumption is that the listeners utility function is a concave transformation of the speakers utility function. This assumption holds vacuously in the binary model. The result that concavity implies credibility allows us to dispense with the assumption that the listeners decision is binary and significantly broadens the scope of the model.

Children's strategic theory of mind.

Significance Human interaction requires reasoning not only about other people’s observed behavior and mental states but also about their incentives and goals. The development of children’s strategic thinking is not well understood, leaving open critical questions about early human capacity for strategic interaction. We investigated strategic reasoning in 3- to 9-y-old children and adults in two strategic games that represent prevalent aspects of social interaction: incentives to mislead and competition. We find that despite strategic differences in the two games, by the age of 7 y, children’s behavior is similar to that of adults. Our findings also show an early sophisticated ability to think strategically about others in both static and repeated interactions. Human strategic interaction requires reasoning about other people’s behavior and mental states, combined with an understanding of their incentives. However, the ontogenic development of strategic reasoning is not well understood: At what age do we show a capacity for sophisticated play in social interactions? Several lines of inquiry suggest an important role for recursive thinking (RT) and theory of mind (ToM), but these capacities leave out the strategic element. We posit a strategic theory of mind (SToM) integrating ToM and RT with reasoning about incentives of all players. We investigated SToM in 3- to 9-y-old children and adults in two games that represent prevalent aspects of social interaction. Children anticipate deceptive and competitive moves from the other player and play both games in a strategically sophisticated manner by 7 y of age. One game has a pure strategy Nash equilibrium: In this game, children achieve equilibrium play by the age of 7 y on the first move. In the other game, with a single mixed-strategy equilibrium, children’s behavior moved toward the equilibrium with experience. These two results also correspond to two ways in which children’s behavior resembles adult behavior in the same games. In both games, children’s behavior becomes more strategically sophisticated with age on the first move. Beyond the age of 7 y, children begin to think about strategic interaction not myopically, but in a farsighted way, possibly with a view to cooperating and capitalizing on mutual gains in long-run relationships.

Persuasion and dynamic communication

A speaker attempts to persuade a listener to accept a request by presenting evidence. A persuasion rule specifies what evidence is persuasive. This paper compares static and dynamic rules. We present a single linear program (i) whose solution corresponds to the listeners optimal dynamic rule and (ii) whose solution with additional integer constraints corresponds to the optimal static rule. We present a condition--foresight--under which the optimal persuasion problem reduces to the classical maximum flow problem. This has various qualitative consequences, including the coincidence of optimal dynamic and static persuasion rules, elimination of the need for randomization, and symmetry of optimal static rules.

Price discrimination through communication

We study a sellers optimal mechanism for maximizing revenue when the buyer may present evidence relevant to the buyers value, or when different types of buyer have a differential ability to communicate. We introduce a dynamic bargaining protocol in which the buyer first makes a sequence of concessions in a cheap talk phase, and then at a time determined by the seller, the buyer presents evidence to support his previous assertions, and then the seller makes a take-it-or-leave-it offer. Our main result is that the optimal mechanism can be implemented as a sequential equilibrium of our dynamic bargaining protocol. Unlike the optimal mechanism to which the seller can commit, the equilibrium of the bargaining protocol also provides incentives for the seller to behave as required. We thereby provide a natural procedure whereby the seller can optimally price discriminate on the basis of the buyers evidence. JEL Code: C78, D82, D83.

Persuasion and Limited Communication

This paper studies optimal persuasion. A speaker must decide which arguments to present and a listener which arguments to accept. Communication is limited in that the arguments available to the speaker depend on her information. Optimality is assessed from the listeners perspective assuming that the listener can commit to a persuasion rule. I show that this seemingly simple scenario--introduced by Glazer and Rubinstein (2006)--is computationally intractable (formally, NP-hard). However under the assumption known as normality, which validates the revelation principle in mechanism design environments with evidence (Green and Laffont 1986, Bull and Watson 2007), I show that the persuasion problem reduces to a classic optimization problem, leading to a simple procedure for its solution. This procedure finds not only the optimal rule, but also the credible implementation of the optimal rule, i.e., the equilibrium of the game without commitment leading to the same outcome as the optimal rule. Normality also has qualitative consequences for the optimal rule. In particular, under normality, there always exists an optimal rule which is symmetric: i.e., ex ante equivalent evidence is treated equivalently. When normality fails, all optimal rules may be asymmetric; in other words, the listener may categorize evidence in an arbitrary manner, and base his decisions on these categories in order to influence the speakers reporting behavior.

Identifying combinatorial valuations from aggregate demand

We study identification of combinatorial valuations from aggregate demand. Each utility function takes as arguments subsets or, alternatively, quantities of the multiple goods. We exploit mathematical insights from auction theory to generically identify the distribution of utility functions. In our setting, aggregate demand for each item is observable while demand for bundles is not. Nevertheless, our identification result allows us to recover the latter.

Neutral Freedom and Freedom as Control

I present a model of freedom as control. Control is measured by the preferences of a decision-maker, or judge, who values flexibility and is neutral towards outcomes ex ante. Formally, I explore the consequences of adding a neutrality axiom to the Dekel, Lipman and Rustichini (2001) axioms for preference for flexibility. I characterize the consensus of all neutral judges about which choice situations embody more freedom. The theory extends the freedom ranking literature to situations where agents have imperfect control, as modeled by choices among lotteries. In a voting context, the consensus of neutral judges coincides with Banzhaf power.

Identification of Demand Models of Multiple Purchases

We study the nonparametric identification of distributions of utility functions in a multiple purchase setting with a finite number of consumers. Each utility function takes as arguments subsets or, alternatively, quantities of the multiple goods. We exploit mathematical insights from auction theory to generically identify the distribution of utility functions. We use price variation and aggregate data on the sales of each product, but not on individual level purchases or the total sales of bundles of products.

Evaluating Allocations of Freedom

This paper develops a formal approach to evaluating freedom in interactive settings based on the literatures on preference for flexibility and measurement of diversity. The approach posits that freedom has an instrumental component -- grounded in preferences -- and an intrinsic component. The philosophical justification and implications of the approach are considered. In particular, I discuss the nature of the required value judgments. Potential conflicts between freedom and efficiency are explored. On a technical level, the paper extends the notion of a diversity measure (Nehring and Puppe 2002) to menus of lotteries, which is what is needed to evaluate freedom when many agents seek flexibility simultaneously.