A Further discussion

We justify the way in which LIO accounts for the cost of incentivization as follows. Fundamentally, the reason is that the cost should be incurred only by the part of the agent that is directly responsible for incentivization. These updates are also used to compute the vector fields shown in Figure 2. With incentives, the players have payoff matrices in Table 2. Table 2: Payoff matrices for row player (left) and column player (right) with incentives. 's expected extrinsic return with respect to agent Hence descending a stochastic estimate of this gradient is equivalent to minimizing the loss in (10).