Dr. Leanne Streekstra

We extend the familiar shortest path problem by supposing that agents have demands over multiple periods. This potentially allows agents to combine their paths if their demands are complementary; for instance if one agent only needs a connection to the source in the summer while the other requires it only in the winter.

We show that the resulting cost sharing problem always has a non-empty core, regardless of the number of agents and periods, the cost structure or the demand profile.

We then exploit the fact that the model encompasses many well-studied problems to obtain or reobtain non-vacuity results for the cores of source-connection problems, (m-sided) assignment problems and minimum coloring problems.

We study electoral competition using a new continuous-time framework for games with a second-mover advantage. Two candidates with different levels of valence and competence in implementing their announced policy, compete for office. There is often a unique (easily calculated) SPNE in which the stronger candidate leads, distorting their policy towards the status quo. In static analogs to this continuous time game, the unique equilibrium is usually in mixed strategies. In our continuous time setting, players never move simultaneously if this involves randomizing over their actions. In this sense, mixed strategy equilibria are an artifact of static games.

We introduce a novel continuous-time framework for analyzing two-player games. Each player can move at most once, choosing an action along with its timing. We extend Simon and Stinchcombe's (1989) results on the relation between discrete and continuous time games by including action sets that are compact subsets of R^n$ (rather than finite). This generalization substantially increases the scope for

applications, where action sets are often intervals. For a class of games where at least one player has a second-mover advantage, we identify a unique subgame perfect Nash equilibrium that entails sequential moves. The identity of the leader can be determined by checking a small set of intuitive conditions. Applications involving price and electoral competition illustrate the power of our modelling approach.

We consider a version of the classic job scheduling problem in which all machines are identical, but in which jobs must be processed before a deadline. We study this problem using cooperative game theory, focusing on the question of how to divide the total cost between the agents. We consider a simple version of the problem, in which all jobs have the same length, and a more general version where jobs of different lengths either need to be processed continuously on one machine or may be interrupted and processed on several machines at the same time. In all these versions the core may be empty. We therefore focus on stability and fairness and define two allocation mechanisms that satisfy the core constraints and either the length-based fair lower bounds or the egalitarian fair lower bounds. For the simple version we also provide necessary and sufficient conditions for the core to be non-empty and for the general version we provide sufficient conditions.

We consider minimum cost spanning tree games with an irreducible cost matrix. We show that these games are a special case of connected balanced games and therefore the existing algorithm for such games can be used to efficiently compute the nucleolus in our case. Moreover, we show that we can reduce the complexity of this algorithm from O(n4) to O(n3), by reducing the size of the input set from n(n+1)/2 to 2n-2.