Sentence examples for at a decision node from inspiring English sources
The edges at a decision node \ v\in V\) are each labeled with actions from a set \ Act\).
This notion of rationality at a decision node \ v\) is forward-looking in the sense that it only takes account of the possibilities that can arise from that point on in the game.
The rationality of a strategy at a decision node depends both on what actions the strategy prescribes at all future decision nodes and what the players know about the strategies that their opponents are following.
So, a player \(i\) is rational at a decision node \ v\in V_i\) in state \(w\) provided that \(i\) does not know that there is an alternative strategy that would give her a higher payoff.
Definition 4.5 (Rationality at a decision node) Player \(i\) is rational at node \ v\in V_i\) in state \(w\) provided, for all strategies \(s_i\) such that \(s_i\ne \sigma_i(w)\), there is an \(o'\in Out_i v, s_i, S_{-i}(w))\) and \(o\in Out_i v, \sigma_i(w), S_{-i}(w))\) such that \ u_i(o)\ge u_i(o')\).
A decision tree starts with a decision node, after which the alternative strategies are depicted.
Recall that a strategy for a player \(i\) specifies choices at all decision nodes for \(i\), even those nodes that are impossible to reach given earlier moves prescribed by the strategy.
Say that a player \(i\) is materially rational at a state \(w\) in an epistemic model of a game if \(i\) is rational at all decision nodes \ v\in V_i\) in state \(w\) that are reachable according to the strategy profile \(\sigma(w)\).
If a patient progresses to the allergy testing limb at the decision node, they will remain in baseline state until the age they are diagnosed with AR, then transition to the nasal steroid state in which they immediately get tested for allergies.
The perceived cost was calculated, and the perceived shortest route was chosen at the decision node.
Similarly, Bob's strategies will be denoted by \(s_B^1=O_2\) and \(s_B^2=I_2\), giving the actions chosen by \(B\) at his decision node.
