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In the case of flipping a coin, flipping a head and flipping a tail are also mutually exclusive events. Both outcomes cannot occur for a single trial (i.e., when a coin is flipped only once). The probability of flipping a head and the probability of flipping a tail can be added to yield a probability of 1: 1/2 + 1/2 =1. [5]
The model used in Aumann [1] to prove the theorem consists of a finite set of states with a prior probability , which is common to all agents. Agent a {\displaystyle a} 's knowledge is given by a partition Π a {\displaystyle \Pi _{a}} of S {\displaystyle S} .
The multiple principal problem, also known as the common agency problem, the multiple accountabilities problem, or the problem of serving two masters, is an extension of the principal-agent problem that explains problems that can occur when one person or entity acts on behalf of multiple other persons or entities. [1]
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If this item is removed, agent does not envy. Additionally, round-robin guarantees that each agent receives the same number of items (m/n, if m is divisible by n), or almost the same number of items (if m is not divisible by n). Thus, it is useful in situations with simple cardinality constraints, such as: assigning course-seats to students ...
Conflict graph: Hummel and Hetland [30] study another setting where there is a conflict graph between items (for example: items represent events, and an agent cannot attend two simultaneous events). They show that, if the degree of the conflict graph is d and it is in (2, n ), then a 1/ d -fraction MMS allocation can be found in polynomial time ...
Key takeaways. In a dual agency situation, the same real estate agent represents both the buyer and the seller of a home. This arrangement can be risky for buyers, since agents are paid based on ...
This rule allows one to express a joint probability in terms of only conditional probabilities. [4] The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.