The cavity method for minority games between arbitrageurs on financial markets

Abstract We use the cavity method from statistical physics for analyzing transient and stationary dynamics of a minority game that is played by agents performing market arbitrage. On level linear response allows to include reaction individual actions as well information items market. This way we derive self-consistent solution game. In particular analyze impact general nonlinear price functions on amount arbitrage if noise external fluctuations present. identify conditions under which gets reduced due presence noise. When extended time dependent previous agents, contributions can be pursued over different scales in until state reached when reached. The are choice strategies. explains evolution scores agents’ strategies: it changes initially random walk non-Markovian bounded excursions an intermediate scale effectively switching between strategies long scales. contrast Curie–Weiss mean-field approach, included captures realistic feature have preference certain without getting stuck single choice. breakdown phase transition region indicates possible mechanisms leading critical volatility regime shift.