Beyond Earthquakes: The New Directions of Expected Utility Theory

Over the past two decades or so, an enormous amount of work has been done to improve the Expected Utility model. Two areas have attracted major attention: the possibility of describing unforeseen contingencies and the need to accommodate the kind of behavior referred to in Ellsberg’s paradox. This essay surveys both.

Simple and Efficient Local Codes for Distributed Stable Network Construction

In this work, we study protocols so that populations of distributed processes can construct networks. In order to highlight the basic principles of distributed network construction we keep the model minimal in all respects. In particular, we assume finite-state processes that all begin from the same initial state and all execute the same protocol (i.e. the system is homogeneous). Moreover, we assume pairwise interactions between the processes that are scheduled by an adversary. The only constraint on the adversary scheduler is that it must be fair. In order to allow processes to construct networks, we let them activate and deactivate their pairwise connections. When two processes interact, the protocol takes as input the states of the processes and the state of the their connection and updates all of them. Initially all connections are inactive and the goal is for the processes, after interacting and activating/deactivating connections for a while, to end up with a desired stable network. We give protocols (optimal in some cases) and lower bounds for several basic network construction problems such as spanning line, spanning ring, spanning star, and regular network. We provide proofs of correctness for all of our protocols and analyze the expected time to convergence of most of them under a uniform random scheduler that selects the next pair of interacting processes uniformly at random from all such pairs. Finally, we prove several universality results by presenting generic protocols that are capable of simulating a Turing Machine (TM) and exploiting it in order to construct a large class of networks.Comment: 43 pages, 7 figure

The "No Justice in the Universe" phenomenon: why honesty of effort may not be rewarded in tournaments

In 2000 Allen Schwenk, using a well-known mathematical model of matchplay tournaments in which the probability of one player beating another in a single match is fixed for each pair of players, showed that the classical single-elimination, seeded format can be "unfair" in the sense that situations can arise where an indisputibly better (and thus higher seeded) player may have a smaller probability of winning the tournament than a worse one. This in turn implies that, if the players are able to influence their seeding in some preliminary competition, situations can arise where it is in a player's interest to behave "dishonestly", by deliberately trying to lose a match. This motivated us to ask whether it is possible for a tournament to be both honest, meaning that it is impossible for a situation to arise where a rational player throws a match, and "symmetric" - meaning basically that the rules treat everyone the same - yet unfair, in the sense that an objectively better player has a smaller probability of winning than a worse one. After rigorously defining our terms, our main result is that such tournaments exist and we construct explicit examples for any number n >= 3 of players. For n=3, we show (Theorem 3.6) that the collection of win-probability vectors for such tournaments form a 5-vertex convex polygon in R^3, minus some boundary points. We conjecture a similar result for any n >= 4 and prove some partial results towards it.Comment: 26 pages, 2 figure