TY - UNPB
T1 - Optimality, Equilibrium, and Curb Sets in Decision Problems without Commitment
AU - Herings, Jean-Jacques
AU - Meshalkin, Andrey
AU - Predtetchinski, Arkadi
PY - 2016/5
Y1 - 2016/5
N2 - The paper considers a class of decision problems with infinite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. We introduce the notions of Nash equilibrium, subgame perfect equilibrium, and curb sets for decision problems. An optimal policy at the initial history is a Nash equilibrium but not vice versa. Both subgame perfect equilibria and curb sets are equivalent to subgame optimal policies. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies.
AB - The paper considers a class of decision problems with infinite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. We introduce the notions of Nash equilibrium, subgame perfect equilibrium, and curb sets for decision problems. An optimal policy at the initial history is a Nash equilibrium but not vice versa. Both subgame perfect equilibria and curb sets are equivalent to subgame optimal policies. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies.
U2 - 10.26481/umagsb.2016021
DO - 10.26481/umagsb.2016021
M3 - Working paper
T3 - GSBE Research Memoranda
BT - Optimality, Equilibrium, and Curb Sets in Decision Problems without Commitment
PB - Maastricht University, Graduate School of Business and Economics
ER -