Achievable Outcomes in Smooth Dynamic Contribution Games

This paper studies a class of dynamic voluntary contribution games in a setting with discounting and neoclassical payoffs (differentiable, strictly concave in the public good, and quasilinear in the private good). An achievable profile is the limit point of a subgame perfect equilibrium path -- the ultimate cumulative contribution vector of the players. A profile is shown to be achievable only if it is in the undercore of the underlying coalitional game, i.e., the profile cannot be blocked by a coalition using a component-wise smaller profile. Conversely, if free-riding incentives are strong enough that contributing zero is a dominant strategy in the stage games, then any undercore profile is the limit of achievable profiles as the period length shrinks. Thus, in this case when the period length is very short, (i) the set of achievable contributions does not depend on whether the players can move simultaneously or only in a round-robin fashion; (ii) an efficient profile can be approximately achieved if and only if it is in the core of the underlying coalitional game; and (iii) any achievable profile can be achieved almost instantly.dynamic games, monotone games, core, public goods, voluntary contribution, gradualism

Smooth Monotone Contribution Games

A monotone game is a multistage game in which no player can lower her action in any period below its previous level. A motivation for the monotone games of this paper is dynamic voluntary contribution to a public project. Each player's utility is a strictly concave function of the public good, and quasilinear in the private good. The main result is a description of the limit points of (subgame perfect) equilibrium paths as the period length shrinks. The limiting set of such profiles is equal to the undercore of the underlying static game - the set of profiles that cannot be blocked by a coalition using a smaller profile. A corollary is that the limiting set of achievable profiles does not depend on whether the players can move simultaneously or only in a round-robin fashion. The familiar core is the efficient subset of the undercore; hence, some but not all profiles that are efficient and individually rational can be nearly achieved when the period length is small. As the period length shrinks, any core profile can be achieved in a “twinkling of the eye” - neither real-time gradualism nor inefficiency are necessary.dynamic games, monotone games, core, public goods, voluntary contribution, gradualism

Achievable Outcomes of Dynamic Contribution Games, Second Version

This paper concerns multistage games, with and without discounting, in which each player can increase the level of an action over time so as to increase the other players’ future payoffs. An action profile is achievable if it is the limit point of a subgame perfect equilibrium path. Necessary conditions are derived for achievability under relatively general conditions. They imply that any efficient profile that is approximately achievable must be in the core of the underlying coalitional game. In some but not all games with discounting, the necessary conditions for achievability are also sufficient for a profile to be the limit of achievable profiles as the period length shrinks to zero. Consequently, in these games when the period length is very short, (i) the set of achievable profiles does not depend on the move structure; (ii) an efficient profile can be approximately achieved if and only if it is in the core; and (iii) any achievable profile can be achieved almost instantly.dynamic games, monotone games, core, public goods, voluntary contribution, gradualism

Information Acquisition and Refunds for Returns

A product exhibits personal fit uncertainty when its consumers have idiosyncratic and uncertain values for it. Often a consumer can learn her long-run value quickly by obtaining the good for a trial period. Money back guarantees of satisfaction are commonly used to lower the cost to consumers of learning their values this way. Increasingly, however, consumers can instead learn about their values before they purchase by, e.g., reading product reviews or consulting experts. We study the effect on a firm’s optimal price and refund of this competing source of information. An efficient outcome would be achieved by setting the refund for a return equal to its salvage value. But a monopoly will, for some parameters, induce consumers to stay uninformed by promising a refund that is greater than the salvage value. This generates an inefficiently large number of returns, which the firm finds worthwhile in order to eliminate the information rents that consumers would obtain by becoming informed. This finding is consistent with the observation that for many products, money back guarantees are generous, as they commonly refund the entire, or almost the entire, purchase price of a product.information acquisition, refunds, money back guarantees, personal fit uncertainty

Information Acquisition and Refunds for Returns

A product exhibits personal fit uncertainty when its consumers have idiosyncratic and uncertain values for it. Often a consumer can learn her long-run value quickly by obtaining the good for a trial period. Money back guarantees of satisfaction are commonly used to lower the cost to consumers of learning their values this way. Increasingly, however, consumers can instead learn about their values before they purchase by, e.g., reading product reviews or consulting experts. We study the effect on a firm’s optimal price and refund of this competing source of information. An efficient outcome would be achieved by setting the refund for a return equal to its salvage value. But a monopoly will, for some parameters, induce consumers to stay uninformed by promising a refund that is greater than the salvage value. This generates an inefficiently large number of returns, which the firm finds worthwhile in order to eliminate the information rents that consumers would obtain by becoming informed. This finding is consistent with the observation that for many products, money back guarantees are generous, as they commonly refund the entire, or almost the entire, purchase price of a product.information acquisition, refunds, money back guarantees, personal fit uncertainty

Information Acquisition and the Excess Refund Puzzle

A buyer can learn her value for a returnable experience good by trying it out, with the option of returning the good for whatever refund the seller offers. Sellers tend to offer a “no questions asked” refund for such returns, a money back guarantee. The refund is often too generous, generating inefficiently high levels of returns. We present two versions of a model of a returnable goods market. In the Information Acquisition Model, consumers are ex ante identical and uninformed of their private values for the good. The firm then offers a generous refund in order to induce the consumers to learn their values by purchasing and trying the good out, rather than by doing costly research prior to purchasing. In the Screening Model, some consumers have negligible costs of becoming informed about their values prior to purchasing, and always do so; other consumers have prohibitive costs of acquiring pre-purchase information and always stay uninformed. The firm’s optimal screening menu may then contain only a single contract, one that specifies a generous refund, and hence a high purchase price, in order to weaken the incentive constraint of the informed consumers.information acquisition, refunds, money back guarantees, returnable experience goods

A Simple Direction Model of Electoral Competition

Examines the use of spatial models in analyzing an electoral process. Conceptualizations of the set of messages that candidates send to voters; Investigations of the optimal strategies of candidates competing against a rigid opponent; Implication of a direction model of the electoral process for a candidate's mobility or voter perception and cognition

Pairwise Symmetry Conditions for Voting Equilibria

Necessary conditions are established for a point contained in the interior or boundary of a convex feasible subset of Euclidean space to be quasi-undominated in an anonymous simple game. Most of the conditions are behaviorally intuitive and imply pariwise symmetries among utility gradients

Undominated Directions in Simple Dynamic Games

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