Figure 4.20: Rejection Rates in Ultimatum Games with and without Responder Competition
This figure presents laboratory evidence from a multi-round experiment, comparing offer rejection rates in ultimatum games based on the size of the offer and the number of Responders. In each round, participants were matched randomly and anonymously. The red bars show the fraction of offers rejected in a standard game with a single Responder, while the blue bars show the rejection fraction when two Responders are in competition. The data illustrates a key finding: individual Responders are less likely to reject offers when competing with another Responder.
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Figure 4.20: Rejection Rates in Ultimatum Games with and without Responder Competition
Imagine a scenario where one person (the 'Proposer') has $100 to split. The Proposer makes a single, simultaneous, take-it-or-leave-it offer to two other people (Person A and Person B). If only one person accepts the offer, they get the offered amount, and the Proposer keeps the rest. If both accept, the Proposer randomly selects one of them to receive the money. If both reject, no one gets anything. Person A strongly believes that Person B is primarily motivated by a sense of fairness and will reject any offer they perceive as insultingly low. How should this belief about Person B influence the minimum offer Person A is willing to accept?
Strategic Decision in a Competitive Ultimatum Game
Responder's Strategy in a Competitive Ultimatum Game
Strategic Thinking in a Competitive Ultimatum Game
True or False: In an ultimatum game where a Proposer makes a single offer to two competing Responders, a Responder who aims to maximize their own monetary payoff should be willing to accept a very low (but non-zero) offer if they believe their competitor will definitely accept that same low offer.
In a scenario where one person (the 'Proposer') offers a split of a sum of money to two competing people (the 'Responders'), a Responder's best strategy depends on their belief about their competitor's motivation. Match each belief a Responder might have about their competitor to the most logical strategic adjustment the Responder should make to their own minimum acceptable offer.
Critique of a Competitive Ultimatum Game Strategy
Analyzing Motivations in a Competitive Bargaining Scenario
Evaluating Strategic Coherence in a Competitive Ultimatum Game
In a one-shot ultimatum game, a Proposer has $20 and makes a single, simultaneous, take-it-or-leave-it offer of $4 to two competing Responders, Sam and Taylor. If only one accepts, they get the $4. If both accept, one is chosen randomly to get the $4. If both reject, no one gets anything. Sam is considering rejecting the $4 offer. Which of the following statements represents the least sound reasoning for Sam's potential rejection?
Figure 4.20: Rejection Rates in Ultimatum Games with and without Responder Competition
Average Offer Size With and Without Responder Competition
Analysis of Economic Decision-Making Under Competition
Consider two variations of a bargaining experiment where a Proposer offers to split a sum of money. In the first setup, there is a single Responder who can accept or reject the offer. In the second setup, two Responders compete; the first to accept the Proposer's offer gets the money. If a Proposer makes a low, unequal offer in both setups, how would the introduction of a competing Responder likely change the outcome?
The Effect of Competition on Bargaining Behavior
In a one-to-one 'take-it-or-leave-it' bargaining scenario, the person receiving the offer holds power because they can veto an unfair deal, forcing the proposer to make a more equitable offer to avoid getting nothing. The introduction of a second, competing recipient for the same offer fundamentally erodes this veto power.
Evaluating the Impact of Competition on Bargaining Power
In a bargaining game, a 'Proposer' offers a split of a sum of money to a 'Responder'. If the Responder accepts, the money is split as proposed; if they reject, neither party receives anything. Match each variation or principle of this game to its most likely corresponding description.
A 'Proposer' is deciding how to split a sum of money in a one-time interaction. In which of the following scenarios should the Proposer, acting to maximize their own share, logically make the lowest offer to the other party/parties?
Analyzing Responder Behavior Under Competition
An experiment is conducted where a 'Proposer' offers to split $10. The Proposer consistently offers $2 to the other participant(s), keeping $8. The experiment is run under two different conditions, and the results for the 'Responders' who receive the offer are recorded in the table below.
Condition Percentage of Responders Accepting the $2 Offer A: One Proposer, One Responder 58% B: One Proposer, Two Competing Responders 90% Based on this data, what is the most logical conclusion about the effect of competition among Responders?
In a bargaining scenario, a single 'Responder' is offered a small, unequal share of a prize by a 'Proposer.' The Responder might reject this offer out of a sense of fairness, even if it means neither party gets anything. Now, imagine the same low offer is made, but there are two Responders, and the first one to accept gets the share. What is the most accurate explanation for why a Responder in this competitive situation is far more likely to accept the low offer?