957 research outputs found
The minimax property in infinite two-person win-lose games
We explore a version of the minimax theorem for two-person win-lose games
with infinitely many pure strategies. In the countable case, we give a
combinatorial condition on the game which implies the minimax property. In the
general case, we prove that a game satisfies the minimax property along with
all its subgames if and only if none of its subgames is isomorphic to the
"larger number game." This generalizes a recent theorem of Hanneke, Livni and
Moran. We also propose several applications of our results outside of game
theory.Comment: 22 page
Dynamic Coordination via Organizational Routines
We investigate dynamic coordination among members of a problem solving team who receive private signals about which of their actions are required for a (static) coordinated solution and who have repeated opportunities to explore different action combinations. In this environment ordinal equilibria, in which agents condition only on how their signals rank their actions and not on signal strength, lead to simple patterns of behavior that have a natural interpretation as routines. These routine spartially solve the team’s coordination problem by synchronizing the team’s search efforts and prove to be resilient to changes in the environment by being expost equilibria, to agents having only a coarse understanding of other agents’ strategies by being fully cursed, and to natural forms of agents’ overcon?dence. The price of this resilience is that optimal routines are frequently not optimal equilibria
The Decision-Conflict and Multicriteria Logit
We study two tractable random non-forced choice models that explain
behavioural patterns suggesting that the choice-deferral outside option is
often selected when people find it hard to decide between the market
alternatives available to them, even when these are few and desirable. The
*decision-conflict logit* extends the logit model with an outside option by
assigning a menu-dependent value to that option. This value captures the degree
of complexity/decision difficulty at the relevant menu and allows for the
choice probability of the outside option to either increase or decrease when
the menu is expanded, depending on *how many* as well as *how attractive*
options are added to it. The *multicriteria logit* is a special case of this
model and introduces multiple utility functions that jointly predict behaviour
in a multiplicative-logit way. Every multicriteria logit admits a simple
discrete-choice formulation
Rationality, decisions and large worlds
Taking Savage's (1954) subjective expected utility theory as a starting point, this thesis distinguishes three types of uncertainty which are incompatible with Savage's theory for small worlds: ambiguity, option uncertainty and state space
uncertainty. Under ambiguity agents cannot form a unique and additive probability function over the state space. Option uncertainty exists when agents cannot assign unique
consequences to every state. Finally, state space uncertainty arises when the state space the agent constructs is not exhaustive, such that unforeseen contingencies
can occur. Chapter 2 explains Savage's notions of small and large worlds, and shows that ambiguity, option and state space uncertainty are incompatible with the small
world representation. The chapter examines whether it is possible to reduce these types of uncertainty to one another. Chapter 3 suggests a definition of objective ambiguity by extending Savage's framework to include an exogenous likelihood ranking over events. The definition
allows for a precise distinction between ambiguity and ambiguity attitude. The chapter argues that under objective ambiguity, ambiguity aversion is normatively permissible.
Chapter 4 gives a model of option uncertainty. Using the two weak assumptions that the status quo is not uncertain, and that agents are option uncertainty averse, we derive status quo bias, the empirical tendency for agents to choose the status quo over other available alternatives. The model can be seen as rationalising status quo bias.
Chapter 5 gives an axiomatic characterisation and corresponding representation theorem for the priority heuristic, a heuristic which predicts binary decisions be-
tween lotteries particularly well. The chapter analyses the normative implications of this descriptive model.
Chapter 6 defends the pluralist view of decision theory this thesis assumes. The chapter discusses possible applications of the types of uncertainty defined in the thesis, and concludes
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