"Game Theory" article on the importance of Stress in Communication by Presh Talwalkar

The sentence “I never said she stole my money” can have 7 different meanings depending on which word you stress. The explicit meanings and possible explanation for why this evolved are below. The potential meanings
I never said she stole my money – the claim wasn’t made by me
I never said she stole my money – I never made the claim
I never said she stole my money – I didn’t utter the claim out loud
I never said she stole my money – possibly someone else stole the money
I never said she stole my money – it could have been a gift
I never said she stole my money – the money was someone else’s
I never said she stole my money – she possibly stole something else
If you consider that multiple words could be stressed, then we have even more meanings. As each word can be stressed or not, there could be as many as 27 = 128 possible ways to stress the sentence, each with slightly different meanings. Why would language develop so that words are ambiguous and defined by context? One possible explanation is fleshed out in a linguistics paper that explains the game between listener and speaker: To understand why ambiguity makes a language more efficient rather than less so, think about the competing desires of the speaker and the listener. The speaker is interested in conveying as much as possible with the fewest possible words, while the listener is aiming to get a complete and specific understanding of what the speaker is trying to say. But as the researchers write, it is “cognitively cheaper” to have the listener infer certain things from the context than to have the speaker spend time on longer and more complicated utterances. The result is a system that skews toward ambiguity, reusing the “easiest” words. Once context is considered, it’s clear that “ambiguity is actually something you would want in the communication system,” Piantadosi says. It seems ambiguity makes for a more efficient language to communicate between two speakers. Here is a link to the full paper: The communicative function of ambiguity in language

Game theory 101 : General Battle

A really weird Soccer Match

Another great post by Presh Talwalkar on a really weird soccer match where both the teams used Game Theory

Yesterday I wrote about a weird World Cup game where nobody tried to score.
There is amazingly an even weirder game on record. The infamous game is about a team advancing in a tournament by scoring an own goal.
In the 1994 Shell Caribbean Cup, Barbados needed two clear goals to advance against Grenada. Losing or winning by one goal meant not advancing. The wrinkle was a rule that goals in overtime would count double to reward a team winning a close game.
The stage was set for an unusual match. Professor Mike Shor of Vanderbilt University writes about the resulting craziness where scoring an own goal was rational:

Barbados needed to win by two goals. With less than ten minutes left in the match, Barbados led by exactly two goals and began to play very defensively. In the 83rd minute, Grenada finally scored, making the score 2-1. Barbados tried to answer but, with only three minutes remaining, was unable to score. Members of the Barbados team contemplated their options. To advance, they needed either to score one more goal in the last three minutes (winning by two), or force the game to extra time where a goal would count as if they won by two. Barbados scored on their own net, tying the game at 2-2.
This is not yet the odd part of the match. The Grenada players, initial shock abating, developed their own strategy. If they could score on Barbados in the waning minutes, they would win the match and advance. But, if they could score a goal on themselves, they would lose by one goal which was still enough to advance. For two minutes, Grenada tried to score on either goal, with Barbados players split between defending their own goal and that of their opponents!
Normal time ended in a tie and the game did go to overtime, in which Barbados scored a game winner and advanced
[emphasis mine]

Professor Shor’s cleverly dubbed the game “which goal is mine.”
Barbados managed to advance but it was eliminated in the next round. No penalties were given to either team since they were both trying to win (albeit in an odd way akin to the puzzle about fixing a broken bet).
The lesson is that simple and seemingly smart rules can have a devastating impact on competition and good play. And much of this can be anticipated if one uses game theory to consider the incentives by thinking ahead and reasoning backwards.
There is a video which shows highlights and the own goal (sadly it omits the chaos where Grenada tried to score on either goal)