Abstract
Physical interactions between particles are the result of the exchange of gauge bosons. Human interactions are mediated by the exchange of messages, goods, money, promises, hostilities, etc. While in the physical world interactions and their associated forces have immediate dynamical consequences (Newton's laws) the situation is not clear for human interactions. Here we quantify the relative acceleration between humans who interact through the exchange of messages, goods and hostilities in a massive multiplayer online game. For this game we have complete information about all interactions (exchange events) between about 430,000 players, and about their trajectories (movements) in the metric space of the game universe at any point in time. We use this information to derive "interaction potentials" for communication, trade and attacks and show that they are harmonic in nature. Individuals who exchange messages and trade goods generally attract each other and start to separate immediately after exchange events end. The form of the interaction potential for attacks mirrors the usual "hit-and-run" tactics of aggressive players. By measuring interaction intensities as a function of distance, velocity and acceleration, we show that "forces" between players are directly related to the number of exchange events. We find an approximate power-law decay of the likelihood for interactions as a function of distance, which is in accordance with previous real world empirical work. We show that the obtained potentials can be understood with a simple model assuming an exchange-driven force in combination with a distance-dependent exchange rate.