### Introduction

Welcome to the Terminal Games website, produced as part of the Summer 2009 REU at the Center for Discrete Mathematics and Theoretical Computer Science. Click on the links above to read a description of the Terminal Games problem (the major problem I've been working on this summer), see my weekly report on what we've accomplished, read about the Cyclic Games problem (which occupied most of my first two weeks at DIMACS), or view our results (in the form of a powerpoint presentation and a RUTCOR Research Report).

I've included two interesting examples of Terminal Games problems, below. The first is a 7-player, 4-terminal game that can enter an infinite loop (i.e. repeatedly force some player to switch to a favorable position) if the wrong edges are chosen, though a Nash Equilibrium does exist. (One is shown, can you find the other 3?) The 2nd diagram shows a 3-player, 3-terminal game of the sort I've been working on. It too has a Nash Equilibrium, but resists certain types of Typological sorting. Click on either picture to see it enter a cycle.

*Robert Rand*