Theory and Decision最新文献

Philosophers’ two favorite accounts of rational choice, Evidential Decision Theory (EDT) and Causal Decision Theory (CDT), each face a number of serious objections. Especially troubling are the recent charges that these theories are dynamically inconsistent. I note here that, under the epistemic assumptions that validate these charges, every decision theory that satisfies a pair of attractive postulates is doomed to a similar fate and then survey various lessons rational choice theorists might opt to draw from this.

We study n symmetric agents engaged in simultaneous k-dimensional contests. We demonstrate that there is no symmetric pure-strategy equilibrium when there are a sufficient number of agents and a prize is awarded only if the agent wins all k sub-contests. Therefore, intermediate prizes (a prize for a win in a single sub-contest) are required for the existence of symmetric pure-strategy equilibrium. We characterize the symmetric equilibrium for either simultaneous or sequential two-dimensional contests and show that the agents’ expected effort increases with the value of the intermediate prizes, and that when there are more than two agents, the optimal total effort in both types of contests is the same.

This paper explores a scenario where a decision maker evaluates bundles by adding up the utility of the options that attract her attention. We introduce a novel attention rule called the “idempotent attention rule” and examine additive representations under this rule. With idempotent attention rules, we can narrow our focus to a subset of bundles to reveal attention rules and utility functions. As a generalization of attention filters, this rule sheds light on how alternatives interact in forming attention.

Khmelnitskaya and Yanovskaya (Math Methods Oper Res 66(2):255–261, 2007) characterized the Owen value for TU games with a coalition structure by the axioms of efficiency, marginality, symmetry across coalitions and symmetry within coalitions. Symmetry across components requires that components with equally productive in the game between components obtain the same total payoffs of their members. In this note, inspired by Casajus (Econ Lett 169:59–62, 2018), we weaken the symmetry across components to the sign symmetry across components, which requires only that equally productive components obtain the same sign of total payoffs. We extend the Khmelnitskaya-Yanovskaya’s characterization by using efficiency, marginality, sign symmetry across coalitions, and sign symmetry within coalitions, similarly as it was done by Casajus (Econ Lett 169:59–62, 2018) for the Shapley value for general TU games. At last, we extend the main result to the Winter value for games with level structure

Features of graphs that hinder finding closed paths with particular properties, as represented by the Traveling Salesperson Problem—TSP, are identified for three classes of graphs. Removing these terms leads to a companion graph with identical closed path properties that is easier to analyze. A surprise is that these troubling graph factors are precisely what is needed to analyze certain voting methods, while the companion graph’s terms are what cause voting theory complexities as manifested by Arrow’s Theorem. This means that the seemingly separate goals of analyzing closed paths in graphs and analyzing voting methods are complementary: components of data terms that assist in one of these areas are the source of troubles in the other. Consequences for standard decision methods are in Sects. 2.5, 3.7 and the companion paper (Saari in Theory Decis 91(3):377–402, 2021). The emphasis here is on paths in graphs; incomplete graphs are similarly handled.

We formulate and analyze market network systems parallel to market games in game theory. We study the structure of efficient and core networks in market network systems. More specifically, we show that if there is no trading cost, a complete network with type-based egalitarian allocations appears in the core of market network systems. Moreover, with heterogeneous trading costs, we show that an efficient network must take the form of a star network with the least-cost-trader as its central player and that the star network is the unique core network.

This paper investigates a two-player contest with a multiplicative sabotage effect, showing it can be converted into a standard Tullock contest with a nonlinear, endogenous cost function. We prove the existence and uniqueness of a pure strategy equilibrium. Our findings suggest that sabotage activities can be more pronounced when the productivity difference between players is small, and the more productive player might not necessarily undergo more attacks. Lazear and Rosen (1981) first-best outcome is attainable for symmetric players if sabotage is sufficiently ineffective or costly. When it is unattainable, optimal pay difference induces positive sabotage only if sabotage is ineffective but relatively inexpensive. Optimal pay difference decreases with effectiveness and increases with the marginal cost of destructive effort, exhibiting a non-monotonic relationship with productive-effort effectiveness. This non-monotonicity contrasts with the monotonicity of the first best pay difference when sabotage is infeasible.

This paper presents a new representation of preference orderings for the study of ambiguity-related decision-making. The central feature is a preference-based decomposition of subjective probabilities that provides information about inherent ambiguity. The probability decomposition is combined with a utility function reflecting the decision-maker’s attitude toward ambiguity. The proposed theory generalizes Savage’s SEU and allows for a straightforward measurement of ambiguity and ambiguity aversion while keeping concepts for measuring risk and risk attitudes unaffected. For the measurement of ambiguity, concepts of probability theory can be used since decision acts can be interpreted as two-dimensional probability distributions. The proposed measure of ambiguity aversion exploits the properties of the utility function in the same way as the Arrow/Pratt measure of risk aversion.

This note discusses the relationship between AU Introspection (i.e., an agent is unaware of some event, then she is unaware of that she is unaware of the event) and Symmetry (i.e., an agent is unaware of some event if and only if she is unaware of the complement set) for non-trivial unawareness (i.e., there is an event an agent is unaware of). without Negative Introspection using a set-theoretical approach in standard state-space models. Previous studies have explored the equivalence between Negative Introspection and AU Introspection, or the equivalence between Negative Introspection and Symmetry, by assuming Necessitation of the knowledge operator. As a corollary, AU Introspection is equivalent to Symmetry. However, no studies have shown the relationship between AU Introspection and Symmetry without Necessitation. Therefore, we explore this issue. Our main result shows that if the knowledge operator satisfies Monotonicity, Truth, and Positive introspection, then Modica and Rustichini’s definition of unawareness leads to the equivalence of AU Introspection and Symmetry. In other words, we show that both AU Introspection and Symmetry hold without clashing with non-trivial unawareness.

Cooperation among firms is governed by contracts. An interesting phenomenon is that some contracts are comprehensive while some are limited. This study tries to explain different levels of the incompleteness of contracts that firms choose to govern their cooperation with. We find that a limited contract is more efficient than a comprehensive contract if partners are highly disparate or product quality is largely uncertain, and vice versa. In contrast, if there are private information and incentives to invest in quality, a comprehensive contract is likely to be more efficient. These findings offer an understanding as to why incomplete contracts are so popular in practice.