scholarly journals Monty Hall three door ’anomaly’ revisited: a note on deferment in an extensive form game

2021 ◽  
Author(s):  
Philipp E. Otto
Keyword(s):  
Probability Theory ◽  
Decision Problems ◽  
Extensive Form ◽  
Form Game ◽  
Information Updating ◽  
Extensive Form Game ◽  
Monty Hall ◽  
Initial Choice

AbstractThe Monty Hall game is one of the most discussed decision problems, but where a convincing behavioral explanation of the systematic deviations from probability theory is still lacking. Most people not changing their initial choice, when this is beneficial under information updating, demands further explanation. Not only trust and the incentive of interestingly prolonging the game for the audience can explain this kind of behavior, but the strategic setting can be modeled more sophisticatedly. When aiming to increase the odds of winning, while Monty’s incentives are unknown, then not to switch doors can be considered as the most secure strategy and avoids a sure loss when Monty’s guiding aim is not to give away the prize. Understanding and modeling the Monty Hall game can be regarded as an ideal teaching example for fundamental statistic understandings.

scholarly journals Secure Degrees of Freedom in Networks with User Misbehavior

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 945
Author(s):  
Karim Banawan ◽  
Sennur Ulukus
Keyword(s):  
Secure Communication ◽  
Multiple Access ◽  
Degrees Of Freedom ◽  
Broadcast Channel ◽  
Interference Channel ◽  
Extensive Form ◽  
Wiretap Channel ◽  
Form Game ◽  
Cooperative Jamming ◽  
Extensive Form Game

We investigate the secure degrees of freedom (s.d.o.f.) of three new channel models: broadcast channel with combating helpers, interference channel with selfish users, and multiple access wiretap channel with deviating users. The goal of introducing these channel models is to investigate various malicious interactions that arise in networks, including active adversaries. That is in contrast with the common assumption in the literature that the users follow a certain protocol altruistically and transmit both message-carrying and cooperative jamming signals in an optimum manner. In the first model, over a classical broadcast channel with confidential messages (BCCM), there are two helpers, each associated with one of the receivers. In the second model, over a classical interference channel with confidential messages (ICCM), there is a helper and users are selfish. By casting each problem as an extensive-form game and applying recursive real interference alignment, we show that, for the first model, the combating intentions of the helpers are neutralized and the full s.d.o.f. is retained; for the second model, selfishness precludes secure communication and no s.d.o.f. is achieved. In the third model, we consider the multiple access wiretap channel (MAC-WTC), where multiple legitimate users wish to have secure communication with a legitimate receiver in the presence of an eavesdropper. We consider the case when a subset of users deviate from the optimum protocol that attains the exact s.d.o.f. of this channel. We consider two kinds of deviation: when some of the users stop transmitting cooperative jamming signals, and when a user starts sending intentional jamming signals. For the first scenario, we investigate possible responses of the remaining users to counteract such deviation. For the second scenario, we use an extensive-form game formulation for the interactions of the deviating and well-behaving users. We prove that a deviating user can drive the s.d.o.f. to zero; however, the remaining users can exploit its intentional jamming signals as cooperative jamming signals against the eavesdropper and achieve an optimum s.d.o.f.

Do supermajority rules really deter extremism? the role of electoral competition

2021 ◽  
pp. 095162982110611
Author(s):  
Daiki Kishishita ◽  
Atsushi Yamagishi
Keyword(s):  
Electoral Competition ◽  
Symmetric Equilibrium ◽  
Extensive Form ◽  
Legislative Voting ◽  
Form Game ◽  
Voting Rule ◽  
Extensive Form Game

This study investigates how supermajority rules in a legislature affect electoral competition. We construct an extensive-form game wherein parties choose policy platforms in an election. Post election, the policy is determined based on a legislative voting rule. At symmetric equilibrium, supermajority rules induce divergence of policy platforms if and only if the parties are sufficiently attached to their preferred platform. Thus, supermajority rules may not always lead to moderate policies once electoral competition is considered.

Stochastic Policies for Games in Extensive Form

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Probability Distribution ◽  
Saddle Point ◽  
Extensive Form ◽  
Form Game ◽  
Expected Outcome ◽  
Recursive Computation ◽  
Extensive Form Game ◽  
Saddle Point Equilibrium ◽  
Computation Of Equilibria ◽  
Game Representation

This chapter discusses two types of stochastic policy for extensive form game representation as well as the existence and computation of saddle-point equilibrium. For games in extensive form, a mixed policy corresponds to selecting a pure policy in random based on a previously selected probability distribution before the game starts, and then playing that policy throughout the game. It is assumed that the random selections by both players are done statistically independently and the players will try to optimize the expected outcome of the game. After providing an overview of mixed policies and saddle-point equilibria, the chapter considers the behavioral policy for games in extensive form. It also explores behavioral saddle-point equilibrium, behavioral vs. mixed policy, recursive computation of equilibria for feedback games, mixed vs. behavioral order interchangeability, and non-feedback games. It concludes with practice exercises and their corresponding solutions, along with additional exercises.

Modeling competitive situations

2020 ◽  
pp. 355-386
Author(s):  
David M. Kreps
Keyword(s):  
Normal Form ◽  
Noncooperative Game ◽  
Extensive Form ◽  
Game Tree ◽  
Decision Node ◽  
Form Game ◽  
Normal Form Game ◽  
Form Representation ◽  
Information Sets ◽  
Extensive Form Game

This chapter studies how competitive situations are conventionally modeled in noncooperative game theory. It uses two sorts or forms of models: the so-called extensive form game and the normal or strategic form game. An extensive form representation of a noncooperative game is composed of the following list of items: a list of players; a game tree; an assignment of decision nodes to players or to nature; lists of actions available at each decision node and a correspondence between immediate successors of each decision node and available actions; information sets; an assignment of payoffs for each player to terminal nodes; and probability assessments over the initial nodes and over the actions at any node that is assigned to nature. There is no single way to proceed in general from a normal form game to a corresponding extensive form game. In one obvious extensive form, the players all choose complete strategies simultaneously, but often other extensive forms could be constructed from a given normal form.

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