This paper considers resource allocation in a network with mobile agents competing for computational priority. We formulate this problem as a multi-agent game with the players being agents purchasing service from a common server. We show that there exists a computable Nash equilibrium when agents have perfect information into the future. From our game, we build a market-based CPU allocation policy and a strategy with which an agent may plan its expenditures for a multi-hop itinerary. We simulate a network of hosts and agents using our strategy to show that our resource-allocation mechanism effectively prioritizes agents according to their endowments and that our planning algorithm handles network delay gracefully.