Battle Sequences Research Articles

The dynamics of majoritarian Blotto games

We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player's overall budget. As a consequence, a player's chance of winning any particular battle is independent of the battlefield and of the number of victories and losses the player has accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either fixed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the payoff structure in this extended game resembles an all-pay auction without noise.

Sequential Majoritarian Blotto Games

We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player's overall budget. As a consequence, a player's chance of winning any particular battle is independent of the battle field and of the number of victories and losses the player accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either fixed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the payoff structure in this extended games resembles an all-pay auction without noise.

Sequential Majoritarian Blotto Games

We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player’s overall budget. As a consequence, a player’s chance of winning any particular battle is independent of the battlefield and of the number of victories and losses the player accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either fixed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the payoff structure in this extended games resembles an all-pay auction without noise.

The Semiotics of Strategy: A Preliminary Structuralist Assessment of the Battle-Map in <em>Patton</em> (1970) and <em>Midway</em> (1976)

This essay offers a preliminary examination of the battle-map as depicted in two films about the Second World War: Franklin J. Shaffner's biopic Patton (1970) and Jack Smight's epic Midway (1976). In these films, maps, charts, or tableaux (the three-dimensional models upon which are plotted the movements of battalions, fleets, and so on) emerge as an expression of both martial and cinematic strategy. It is argued that the battle-map emerges as a crucial isomorphic element. It features as a prop to signify command and to relay otherwise complex strategic plottings, giving audiences a glimpse into how military strategy is formed and tested: a traditional 'reading' of the map. Conversely, the map is a device of foreshadowing and a sign of command's profound limitations. It is thus resolved that the battle-map is as much a sign of the subjective as the objective.

The Armed Peace: A Punctuated Equilibrium Theory of War

According to a leading rationalist explanation, war can break out when a large, rapid shift of power causes a credible commitment problem. This mechanism does not specify how inefficient fighting can resolve this cause, so it is an incomplete explanation of war. We present a complete information model of war as a sequence of battles and show that although opportunities for a negotiated settlement arise throughout, the very desirability of peace creates a commitment problem that undermines its likelihood. Because players have incentives to settle as soon as possible, they cannot credibly threaten to fight long enough if an opponent launches a surprise attack. This decreases the expected duration and costs of war and causes mutual deterrence to fail. Fighting's destructiveness improves the credibility of these threats by decreasing the benefits from continuing the war and can eventually lead to peace. In equilibrium players can only terminate war at specific windows of opportunity and fighting results in escalating costs that can leave both players worse off at the time peace is negotiated than a full concession would have before the war began.

Mountbatten goes to the movies: Promoting the heroic myth through cinema

Mountbatten goes to the movies: Promoting the heroic myth through cinema

Equilibrium and Efficiency in the Tug-of-War

We characterize the unique Markov perfect equilibrium of a tug-of-war without exogenous noise, in which players have the opportunity to engage in a sequence of battles in an attempt to win the war. Each battle is an all-pay auction in which the player expending the greater resources wins. In equilibrium, contest effort concentrates on at most two adjacent states of the game, the tipping states, which are determined by the contestants' relative strengths, their distances to final victory, and the discount factor. In these states battle outcomes are stochastic due to endogenous randomization. Both relative strength and closeness to victory increase the probability of winning the battle at hand. Patience reduces the role of distance in determining outcomes. Applications range from politics, economics and sports, to biology, where the equilibrium behavior finds empirical support: many species have developed mechanisms such as hierarchies or other organizational structures by which the allocation of prizes are governed by possibly repeated conflict. Our results contribute to an explanation why. Compared to a single-stage conflict, such structures can reduce the overall resources that are dissipated among the group of players.

D-Day Filming - For Real. A Comparison of ?Truth? and ?Reality? inSaving Private Ryanand Combat Film by the British Army's Film and Photographic Unit

S teven Spielberg's Saving Private Ryan (1998) is acclaimed for its realistic battle sequences. In part Spielberg achieved this realism by mimicking the style of combat film shot by Allied cameramen. But how does this representation compare with the real thing, taken by men under fire using basic, cumbersome cameras? The purpose of this article is to explore these differences and evaluate how these two different cinematic approaches contribute to our understanding of the Normandy campaign and warfare in general. The release of Saving Private Ryan is regarded as a landmark in the history of war films, because of the visceral power and brutal realism of its treatment of combat, particularly in the opening 26 minutes which covers the landing of US soldiers on the 'Omaha' sector of the Normandy beachhead. For film archivists and historians privileged with an intimate knowledge of the film and photographs taken by official cameramen serving with the soldiers at Normandy, the hyperbole surrounding the release of Saving Private Ryan offered a fascinating opportunity to compare the feature film version with the 'real footage'.1 Not only was this an interesting exercise in itself but it provided a context in which to screen this extraordinary official film in its unedited and mute state. Most members of the general public are scarcely aware that cameramen filmed at D-Day and their only opportunity to view this film would have been when it was incorporated in wartime newsreels or, more likely, in short and oft-repeated sequences used in television documentaries. The public was given this opportunity at two lectures I presented on behalf of the Imperial War Museum, at the Museum of the Moving Image and the Imperial War Museum, entitled 'D-Day Filming for Real'. 2 These lectures involved screening the first 26 minutes of Saving Private Ryan, followed by sequences of official combat film taken by American and British cameramen, concentrating on the reels shot by the British cameramen of the Army Film and Photographic Unit (AFPU) who landed on the Sword and Juno sectors of the Normandy beachhead. As with the lectures, this paper will begin with a discus-

The great war

Abstract These stereo cards are from the set ‘The Great War’, published by H. D. Girdwood, ca. 1917 The 200-card set, one of his ‘Realistic Travels’ series, covered the 1914/16 period of the war, and most of them authentically show troop mobilization and movement, the effects of bombardments, parades, etc. However, during these years, photography at the actual battle fronts was subject to severe censorship and control, and so approximately fifty of the cards in the set which purport to show events at the front line, on closer examination, portray something rather different. Most, if not all, of these battle sequences were obviously staged, at locations far from the front. ‘Corpses’ are placed in picturesque attitudes of death, the trenches are neat, practice ones set in placid, undisturbed landscapes, and the troops are immaculately turned out. The term ‘Theatres of War’ takes on an unintentiOnal meaning, as it is indeed in the dramatic theatrical sense that these battle sequences are staged.