For each interaction we randomly select two agents i, j and compare their opinions.
Consider two neighboring agents i and j with opinions as x i and x j, respectively.
There exists an edge ( i, j ) ∈ E between agents i and j if they can directly communicate with each other.
If agents i and j are connected through a communication line, α ij ≠ 0, otherwise, α ij = 0.
TB-ADM is well suited for decentralized computation since the updates require only communication between agents i and j, who are one-hop neighbors.
Practically, suppose that two agents i and j are respectively in state (mathbf{x}_{i}^{(t)}) and (mathbf{x}_{j}^{(t)}) at time t.
This requires that there exists a pair of agents (i, l) such that the shortest path between them is of length 3.
Therefore, suppose that (a^k_i), (a^k_j) are two single number values on the features (a^k), of two agents (i) and (j), respectively.
In practice, this means that when agents i and j interact, the probability that j changes its self-appreciation depends on agent i's self-appreciation, through (p_{ij}), which determines whether or not an initiated event leads to any change.
There do not exist agents (i,jin [0,1]) such that agent i's equilibrium expected utility is monotone increasing in enforcement expenditure c (fine f) whereas agent j's equilibrium expected utility is monotone decreasing in enforcement expenditure c (fine f).
Every vertex of the ambiguity graph is uniquely identified by the notation vi,j l,r), where i and j refer to agents i and j and l and r refer to their respective lth and rth measurements.
