Bachelor of Arts
Game theory, Graphs, Theoretical computer science
In the same way that traditional game theory captured the minds of economists and allowed complex problems to be studied using simple models, so have games on networks come to be used in computer science. In particular, previous work has focused on extending a two-player base game M over a network G by having each vertex in G chose a strategy from the base game and play it simultaneously against all adjacent nodes. Similarly, the utility for each vertex becomes the sum of the utility of that node in each of the games it plays against its neighbors. The resulting networked game is called M + G. This paper seeks to augment the body of existing work by studying a few similar networked games and finding key characteristics like the existence of Nash equilibria, the price of anarchy, the price of stability, the convergence speed of best response dynamic, and the difficulty of finding the optimal solution. We also reproduce the result that the class of exact potential games is isomorphic to the class of congestion games with a proof that is drastically more readable than the original. Co-authored by Tom Wexler.
Kimmel, Jason, "Simple Games on Networks" (2011). Honors Papers. 416.