Research was undertaken with the goal of applying general universally-applicable induction methods to complex real-world problems. The goal was only partially met. The chosen domain-the card game Eleusis-was still somewhat artificial, and the universally-applicable induction methods were found to be lacking in important ways. However, the resulting Eleusis program does show that by using knowle...

We apply backward induction to derive optimal price functions. In the second period, given first period price p 1 , the firm selects second period price p 2 (p 2 < Max{q, R}) to maximize its second period profit: The profit function can be reduced to four possibilities based on the value of p 1 : By maximizing profit in each of the four cases, we can derive the optimal second period price p 2 a...

Some very difficult questions in finite geometry (for example, concerning ovoids, spreads, and extensions) have fairly trivial resolutions in the infinite case, by standard transfinite induction. We give some old and new results of this kind, and a number of open questions. The paper is expository in nature, and is intended to illustrate the technique rather than give the most general applicati...

Finite perfect information extensive (FPIE) games are quite well-understood: backward induction yields all of the pure strategy subgame perfect equilibria of such games. Iterative elimination of weakly dominated strategies (IEWDS), which can be hazardous in general games due to orderdependence of outcomes, can be much better behaved. In fact, for a large class of FPIE games, the outcomes of IEW...

Consider a coaction δ of a locally compact group G on a C-algebra A, and a closed normal subgroup N of G. We prove, following results of Echterhoff for abelian G, that Mansfield’s imprimitivity between A ×δ| G/N and A ×δ G ×δ̂,r N implements equivalences between Mansfield induction of representations from A×G/N to A×G and restriction of representations fromA×G×rN to A × G, and between restrictio...

The recurrence is significant since if we set ai = 0, bi = i for all i we get the Stirling numbers of the second kind, and if we set ai = bi = i for all i we get the Lah numbers. The Lah numbers count the partitions of an n-set into blocks of size k in which the numbers in each block are ordered. The proof in [1] involves generating functions and is rather long. Here we give a short induction p...

This paper reports an experiment testing whether strategically equivalent representations of a social situation produce equivalent behavior when actually played by human subjects. The investigation was limited to representative members of the class of generic 2×2 extensive form games of perfect information, which include widely studied games in the experimental literature, and the resulting cla...