Related papers: Extending rational choice behavior: The decision p…
The dominant theories of rational choice assume logical omniscience. That is, they assume that when facing a decision problem, an agent can perform all relevant computations and determine the truth value of all relevant logical/mathematical…
I formulate and characterize the following two-stage choice behavior. The decision maker is endowed with two preferences. She shortlists all maximal alternatives according to the first preference. If the first preference is decisive, in the…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of…
This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
Stalnaker and Thomason famously proved that the conditional logic \textsf{C2} with first-order quantifiers is complete with respect to a selection function semantics. However, the selection functions used in this completeness result take…
In the problem of allocating a single non-disposable commodity among agents whose preferences are single-peaked, we study a weakening of strategy-proofness called not obvious manipulability (NOM). If agents are cognitively limited, then NOM…
Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered around the structure and…
We intend to create new concepts aimed at finding necessary and sufficient conditions for Boolean satisfiability so that these conditions can be verified in polynomial time. Based on these conditions it will be possible to create an…
The Kochen-Specker no-go theorem established that hidden-variable theories in quantum mechanics necessarily admit contextuality. This theorem is formally stated in terms of the partial Boolean algebra structure of projectors on a Hilbert…
This paper explores a new class of incomplete preferences -- termed ``connected preferences'' -- in which maximal domains of comparability are topologically connected. We provide necessary and sufficient conditions for continuous…
Coalition formation is a key problem in automated negotiation among self-interested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can do things more…
A set $R\subset \mathbb{N}$ is called rational if it is well-approximable by finite unions of arithmetic progressions. Examples of rational sets include many classical sets of number-theoretical origin such as the set of squarefree numbers,…
Completeness and transitivity are standard rationality conditions in economics. However, under ambiguity, decision makers sometimes violate these requirements because of the difficulty of forming accurate predictions about ambiguous events.…
Decision procedures can be either theory-specific, e.g., Presburger arithmetic, or theory-generic, applying to an infinite number of user-definable theories. Variant satisfiability is a theory-generic procedure for quantifier-free…
An agent acquires a costly flexible signal before making a decision. We explore to what degree knowledge of the agent's information costs helps predict her behavior. We establish an impossibility result: learning costs alone generate no…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
We show that for any class of Boolean algebras with an associative operator, if it contains the complex algebra of (P(N), U), its equational theory is undecidable. Equivalently, any associative normal modal logic valid over the frame (P(N),…
We introduce a new family of mechanisms for one-sided matching markets, denoted pick-an-object (PAO) mechanisms. When implementing an allocation rule via PAO, agents are asked to pick an object from individualized menus. These choices may…
Sequential allocation is a simple and widely studied mechanism to allocate indivisible items in turns to agents according to a pre-specified picking sequence of agents. At each turn, the current agent in the picking sequence picks its most…