Of course, games are a specific case where the utility (winning) is well-defined, and usually relative to other players, where life is much more complicated, ambiguous, and a mix of competitive and cooperative games.
Lots of board games have badly specified utility functions. The one that springs to mind is Diplomacy; if a stalemate is negotiated then the remaining players "share equally in a draw". I'd take this to mean that each player gets utility 1/n (where there are n players, and 0 is a loss and 1 is a win). But it could also be argued that they each get 1/(2n), sharing a draw (1/2) between them (to get 1/n each wouldn't they have to be "sharing equally in a win"?).
You Play to Win the Game.
Another example is Castle Panic. It's allegedly a cooperative game. The players all "win" or "lose" together. But in the case of a win one of the players is declared a "Master Slayer". It's never stated how much the players should value being the Master Slayer over a mere win.
Interesting situations occur in these games when the players have different opinions about the value of different outcomes. One player cares more about being the Master Slayer than everyone else, so everyone else lets them be the Master Slayer. They think that they're doing much better that everyone else, but everyone else is happy so long as they all keep winning.
In Diplomacy I've never heard the 1/(2n) argument from that sentence. All it's saying is that if you are part of the draw, the person who survived with 1 supply center gets the same result as the one with all 17 on the other side of the line. Whether players actually treat it that way is up to them, of course.
Multiplayer prisoner's dilemma games (with information) are absolutely a situation where I endorse Modesty. Don't play as if you are a special snowflake who is going to bamboozle your opponents. Sometimes you're increasing variance, so that you're more often first place even without raising your average score, but more often you're just shooting yourself in the foot.
If you just play a solid, modest, try-to-cooperate-against-people-who-are-also-trying-to-cooperate-against-this-strategy strategy, what I feel like tends to happen is that some opponents will profit slightly off of playing against you, and then defect a lot against each other because they're trying to be fancy, and then you win.
Edwards responded "This is what's great about sports, the greatest thing about sports is you play to win the game. Hello? You play to win the game. You don't play just to play it. That's the great thing about sports, you play to win. And I don't care if you have any wins. You go play to win. When you start telling me it don't matter, then retire... GET OUT! Because it matters. This whole conversation bothers me."
There is an old saying; "It's not if you win or lose, it's how you play the game." I agree with this statement to an extent. I would rephrase this quote to: "It's not if you win or lose the game, it's how well did you mentally and physically prepare for the game to give it your best shot?" If you prepare yourself and team the best they can be prepared, wins will come. If you simply go through the motions, you are cutting yourself and your team short and there will never be a collective maximum output by the team.
The Patriots certainly could have done themselves a huge favor by figuring out a way to beat the Dolphins. A win would have given them the AFC's top seed and home field advantage throughout the playoffs. A win would have provided at least a little momentum toward a potential post-season run.
Why did the Patriots' game plan call for multiple runs, and only five first half passes? Why was the offense shackled with its lowest yardage total in almost 14 years? And why were Tom Brady and Rob Gronkowski, among others, still in the game in the 4th quarter - then pulled with two minutes to play with a chance to still win?
One-time New York Jets' coach (and current ESPN NFL analyst) Herm Edwards' infamous retort to a question asked of him in a post-game interview in 2002 - "You play to win the game. Hello? You play to win the game. You don't play it to just play it." - comes to mind as you ask yourself just what the Patriots were playing for Sunday afternoon in South Florida, and why they played this game the way they did?
The answer for New England doesn't come as easily as Edwards' long ago quote. Sure, you play to win the game. But you also play with your team's best overall interests in mind. Was it in the Patriots' best interest to treat this game like any other and play full tilt? Or was it in their best interest to play more conservatively - run the ball, run the clock and shorten the game, keep your quarterback on his feet and out of the way of a pass rush?
The trouble is, they couldn't do any of those things particularly well. With the current state of the offensive line being, well, offensive...effective run-blocking and pass-blocking haven't occurred often enough to run, pass or protect well enough to win any game. Sure, injuries have been a major factor with the less-than-satisfactory results, but since when are injuries used as an excuse - even if they ARE an excuse?
Great. But then why were Brady and Gronkowski still in the game well into the 4th quarter, then pulled with two minutes to play in a still-winnable game? And TB12 had already suffered a twisted ankle after taking an earlier hit from Miami's Ndamukong Suh. Legit questions, and undoubtedly, questions that won't provide an answer anyone will understand - or like.
Here's one thought - Miami's defense did a pretty solid job of wrecking whatever plans the Patriots had to win this game, whether the Dolphins had anything to play for or not. Credit is due where it is deserved. Could New England have adjusted the game plan in order to win? Perhaps, but the risk involved outweighed the potential reward in the end.
The most troubling aspect of the result is having now lost four of six games heading into the playoffs. It's un-Patriot-like to have that kind of negative momentum at this stage of a season. It also begs another question - will this recent streak have any effect on the playoffs?
At least that last one now has an answer. As to the others, your guess is as good as anyone's. The reality of it all - there wasn't much to play for Sunday, even if you (allegedly) play to win the game.
Week 17 was the 9th straight week, by this count, that the Patriots played with different starters on the offensive line. There have also been 12 different combinations of starters, so it's fair to say there has been a lack of continuity in an area that requires everyone to be on the same page for maximum production. Can't do a thing about injuries, they are part of the game.
There were also lapses in the secondary on 3rd and long situations (Logan Ryan), and relative newcomer Leonard Johnson was beaten for a 31-yard gain by Greg Jennings. McCourty was a victim playing a two-deep zone on a touchdown play to DeVante Parker, and also gave up a big gain against Parker that set up the eventual go-ahead score.
Now comes the hard part. Can these Patriots pick themselves back up from getting decked, with (or without) key players involved? Are all of the injured eligible to return...going to return? If so, can the offense and defense pick up where they left off two months ago? If not, can this team figure out a way to survive and advance anyway?
Even though he wasn't going to play on Sunday, Cleveland's Johnny Manziel was a no-show for a scheduled meeting with a team doctor. Manziel is technically in the midst of following the NFL's concussion protocol, but his mind is apparently on everything BUT his job.
Rumors persist the Browns are done with his antics, but that will be for a new coach and general manager to decide. Rumors also persist that Manziel wants to play for the Dallas Cowboys, and that Cowboys' owner Jerry Jones would also like to have him as a drawing card as a former Texas Aggie - if nothing else.
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